In [2], Roger Brockett derived a necessary condition for the existence of a feedback control law ... more In [2], Roger Brockett derived a necessary condition for the existence of a feedback control law asymptotically stabilizing an equilibrium for a given nonlinear control system. The intuitive appeal and the ease with which it can be applied have made this criterion one of the standard tools in the study of the feedback stabilizability of nonlinear control systems. Brockett's original proof used an impressive combination of Liapunov theory and algebraic topology, in part to cope with a lacuna in our understanding of the topology of the sublevel sets of Liapunov functions. In [33], F. W. Wilson, Jr. extended the converse theorems of Liapunov theory to compact attractors and proved some fundamental results about the topology of their domain of attraction and the level sets of their Liapunov functions. In particular, Wilson showed that the level sets Mc = V −1 (c) are diffeomorphic to S n−1 for n = 4, 5 using the proof of the generalized Poincaré Conjecture of Smale. He observed that the excluded cases would from the validity of the Poincaré Conjecture in dimension 3 and 4 and showed that, for n = 5, the assertion ∂Mc ≃ S 4 would imply the Poincaré Conjecture for 4-manifolds. Of course, the topological Poincaré Conjecture for S 4 was subsequently proved by Freedman in 1980 and with the remarkable recent solution by Perelman of the classical Poincaré Conjecture, Wilson's Theorem now holds for all n. In this paper we describe the sublevel, and therefore as a corollary the level, sets of proper smooth functions V : R n → R having a compact set C(V) of critical points. Among the main results in this paper is the assertion that an arbitrary sublevel set Mc = V −1 [0, c] of such a function is homeomorphic to D n , the unit disk. For n = 2, this assertion is a consequence of the Schönflies Theorem, a classical enhancement of the Jordan Curve Theorem. For arbitrary n it follows from the generalized Schönflies Theorem of Mazur and Brown, from [33] and from the verification of the Poincaré Conjecture in all dimensions by Perelman, Freedman and Smale. We also describe the smooth structure of Mc and its boundary, generalizing the results of [33]. This result has several corollaries. In particular, using the Brouwer Fixed Point Theorem this gives a straightforward proof of Brockett's criterion and some of its enhancements to global attractors. These results in turn imply a new necessary condition for Input-to State Stability with respect to a compact set and an extension of Brockett's Theorem to the practical stabilizability of equilibria. Our main results can be further enhanced using the Poincaré-Hopf Theorem and, in this way, also lead to a streamlined version of Coron's proof [7] that Brockett's Theorem holds for continuous feedback laws, using a classical topological argument on the unit disc D n. 1. Introduction. Consider a control system (1.1)ẋ = f (x, u) x ∈ R n , u ∈ R m * Dedicated to my friend and teacher, Roger Ware Brockett, on the occasion of his seventieth birthday. Research supported in part by grants from the AFOSR.
Robustness to uncertain parameters of this popular induction motor controller is investigated. Co... more Robustness to uncertain parameters of this popular induction motor controller is investigated. Conditions for local and global asymptotic stability as well as boundedness of all signals are derived
Performance in an engineering system tends to degrade over time due to a variety of wearing or ag... more Performance in an engineering system tends to degrade over time due to a variety of wearing or ageing processes. In supervisory controlled processes there are typically many signals being monitored that may help to characterise performance degradation. It is preferred to select the least amount of information to obtain high quality of predictive analysis from a large amount of collected data, in which labelling the data is not always feasible. To this end a novel unsupervised feature selection method, robust with respect to significant measurement disturbances, is proposed using the notion of "weak monotonicity" (WM). The robustness of this notion makes it very attractive to identify the common trend in the presence of measurement noises and population variation from the collected data. Based on WM, a novel suitability indicator is proposed to evaluate the performance of each feature. This new indicator is then used to select the key features that contribute to the WM of a family of processes when noises and variations among processes exist. In order to evaluate the performance of the proposed framework of the WM and suitability, a comparative study with other nine state-of-the-arts unsupervised feature evaluation and selection methods is carried out on well-known benchmark datasets. The results show a promising performance of the proposed framework on unsupervised feature evaluation in the presence of measurement noises and population variations.
Despite the enormous benefit that has accrued to society from control technology and the continue... more Despite the enormous benefit that has accrued to society from control technology and the continued vitality of control science as a research field, there is broad consensus that the practitioners of control and the academic research community are insufficiently engaged with each other. We explore this concern with reference to the oft-cited theory/practice gap but also from an industry perspective. The core of this article is comprised of ten "messages," targeting primarily researchers interested in the practical impact of their work, that we hope shed insight on industry. Results from surveys and other data are cited to underpin the points. Some educational synergies between industry and academia are also noted. To highlight the continuing relevance of control science to industry, several recent examples of successful, deployed advanced control solutions are presented. The authors of this article are members of the IFAC Industry Committee, formally established in 2017 with objectives that include (per the updated IFAC Constitution) "increasing industry participation in and impact from IFAC activities."
Evaluating progress throughout a patient’s rehabilitation episode is critical for determining eff... more Evaluating progress throughout a patient’s rehabilitation episode is critical for determining effectiveness of the selected treatments and contributing to the evidence-based practice. The evaluation process is complex due to the inherent large human variations in motor recovery and the limitations of commonly used clinical measurement tools. Information recorded during a robot-assisted rehabilitation process can provide an effective means to continuously quantitatively assess movement performance and rehabilitation progress. However, selecting appropriate motion features for rehabilitation evaluation has always been challenging. This paper exploits unsupervised feature learning techniques to reduce the complexity of building the evaluation model of patients’ progress. A new feature learning technique is developed to select the most significant features from a large amount of kinematic features measured from robotics, providing clinically useful information to health practitioners wi...
Stability and performance of networked control systems has been a recent area of interest in the ... more Stability and performance of networked control systems has been a recent area of interest in the control literature. The inclusion of a shared communication network between plant and controller inevitably leads to occasional random data loss. We provide novel results relating to the probability of such a system being globally asymptotically stable or input to state stable.
Proceedings of the 15th IFAC World Congress, 2002, 2002
In this paper, an aircraft landing autopilot is designed using the nonlinear energybased control ... more In this paper, an aircraft landing autopilot is designed using the nonlinear energybased control method (NEM). This method provides the automatic landing by energy management idea. Using the NEM the stabilization and tracking can be achieved by modifying the energy functions. The method is illustrated on an automatic landing system problem for a twinengine civil aircraft, developed by Group for Aeronautical Research and Technology in Europe (GARTEUR). Further we provide physical interpretation of the control laws. A disturbance rejection and robustness analysis is also performed via numbers of simulations at extreme flight conditions. The proposed control laws behave well even under extreme flight conditions.
The stability of the signed regressor variant of least mean square (LMS) adaptation is found to b... more The stability of the signed regressor variant of least mean square (LMS) adaptation is found to be heavily dependent on the characteristics of the input sequence. Averaging theory is used to derive a persistence of excitation condition which guarantees exponential stability of the signed regressor algorithm. Failure to meet this condition (which is not equivalent to persistent excitation for LMS) can result in exponential instability, even with the use of leakage. This new persistence of excitation condition is then interpreted in both deterministic and stochastic settings.
A novel approach to finding an approximate analytic solution to the Bloch equation is developed i... more A novel approach to finding an approximate analytic solution to the Bloch equation is developed in this paper. The method is based on time scaling and averaging of the Bloch equation after transformation to a rotating frame of reference. In order to accomplish the scaling, a novel time scaled magnetisation vector is introduced. The resultant time scaled system is subsequently approximated through averaging, a technique that to the best of our knowledge, has not previously been applied in the nuclear magnetic resonance context. Our proposed method of approximating the solution to the Bloch equation is valid for continuous wave excitation as well as the traditional pulse excitation with an arbitrary envelope, making this a widely applicable technique unlike previously proposed methods. Comparison of the approximate analytic solution and simulation results clearly indicates that the error is negligible when the field inhomogeneities are small compared to the excitation field amplitude. Extremum seeking techniques may be applied to determine the optimal excitation, given the form of the approximate solution. This result is applicable to a range of research areas including nuclear magnetic resonance, magnetic resonance imaging and optical resonance problems.
Thr paper presents nonlinear averaging theorems lor two-time scale systems, where the dynamics of... more Thr paper presents nonlinear averaging theorems lor two-time scale systems, where the dynamics of the fast system are allowed to vary with the slow system. The results are &lied to the Narendra-Valavani adaplive canlrol algorithm, and estimates of the parameter convergence rates are obtained which d o not rely a n a linearization of the system around the cquilibriurn. and therciore arc valid in a larger region in the parameter space.
Output dead beat control for a class of non linear discrete time systems, which are described by ... more Output dead beat control for a class of non linear discrete time systems, which are described by a single input-output polynomial difference equation, is considered. The class of systems considered is restricted to systems with a two dimensional state space description. It is assumed that the highest degree with which the present input appears in the equation is odd. Necessary and sufficient conditions for the existence of output dead beat control and for the stability of the zero output constrained dynamics are presented. We also design a minimum time output dead beat control algorithm (feedback controller) which yields stable zero dynamics, whenever this is feasible. A number of interesting phenomena are discussed and illustrated by examples.
Mathematics of Control, Signals, and Systems, 1988
For continuous-time, multiple-input, multiple-output, linear systems, we present conditions under... more For continuous-time, multiple-input, multiple-output, linear systems, we present conditions under which the persistency of excitation of one regression vector implies the persistency of another regression vector derived from the first via a linear, dynamical transformation. We then introduce a definition of sufficient richness for vector input signals in the form of a persistency of excitation condition on a basis regression vector. Finally we establish input conditions which guarantee the persistency of excitation of a large class of regression vectors obtained from both time-invariant and time-varying systems.
Mathematics of Control, Signals, and Systems, 1997
We propose and analyse a populational version of stepwise gradient descent suitable for a wide ra... more We propose and analyse a populational version of stepwise gradient descent suitable for a wide range of learning problems. The algorithm is motivated by genetic algorithms which update a population of solutions rather than just a single representative a s i s t ypical for gradient descent. This modi cation of traditional gradient descent (as used for example in the backpropagation algorithm) avoids getting trapped in local minima. We use an averaging analysis of the algorithm to relate its behaviour to an associated ordinary di erential equation. We d e r i v e a result concerning how long one has to wait in order that with a given high probability, the algorithm is within a certain neighbourhood of the global minimum. We also analyse the e ect of di erent population sizes. An example is presented which corroborates our theory very well.
International Journal of Adaptive Control and Signal Processing, 1992
This paper addresses certain functional learning tasks in signal processing using familiar algori... more This paper addresses certain functional learning tasks in signal processing using familiar algorithms and analytical tools of least squares for autoregressive moving average exogonous input (ARM AX) models. The models can be viewed as conventional ARM AX models but with parameters dependent on variables such as inputs or states. termed function input variables. The functional dependence of the parameters on these variables is represented in terms of basis function expansions, or more generaliv int erpoiation function representations. The interpolation functions in a least squares identification of coefficients also turn out to be in essence spread functions that spread learning throughout the space of function input variables. Thus for a set of training sequences. or trajectories in function input space, system parameters and thereby system functional can be updated. The idea is that these will have relevance for similar sequences or neighboring trajectories. The concept of persistence of excitation to achieve complete function learning, or equivalently, signal model learning is studied using least squares convergence results. Application of the proposed algorithms and theory within the signal processing context is addressed by means of simple illustrative examples. q Work partially supported by Boeing (BCAC).
In this paper, we address the problem of reduced-complexity estimation of general large-scale hid... more In this paper, we address the problem of reduced-complexity estimation of general large-scale hidden Markov models (HMMs) with underlying nearly completely decomposable discrete-time Markov chains and finite-state outputs. An algorithm is presented that computes () (where is the related weak coupling parameter) approximations to the aggregate and full-order filtered estimates with substantial computational savings. These savings are shown to be quite large when the chains have blocks with small individual dimensions. Some simulation studies are presented to demonstrate the performance of the algorithm.
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1997
In the literature on dynamical systems analysis and the control of systems with complex behavior,... more In the literature on dynamical systems analysis and the control of systems with complex behavior, the topic of synchronization of the response of systems has received considerable attention. This concept is revisited in the light of the classical notion of observers from (non)linear control theory.
Dead-beat controllers for simple Hammerstein systems are investigated. Several designs for nonmin... more Dead-beat controllers for simple Hammerstein systems are investigated. Several designs for nonminimum-time state dead-beat controllers are given for certain classes of simple Hammerstein systems. A general minimum-time state dead-beat controller is presented for a class of simple Hammerstein systems. A design for a family of minimum-time control laws is provided. This enables, to a certain extent, shaping of transient response via choosing an appropriate control law. Finally, the authors design an output dead-beat controller for a class of Hammerstein systems that are not necessarily state dead-beat controllable.
Output deadbeat control in one step is considered for a class of discrete-time systems described ... more Output deadbeat control in one step is considered for a class of discrete-time systems described by a nonlinear single-input/singleoutput recursive representation. Global stability conditions are established for the particular subclass of systems with one-dimensional zero dynamics. The results are illustrated with applications to polynomial and neural dynamical systems.
In [2], Roger Brockett derived a necessary condition for the existence of a feedback control law ... more In [2], Roger Brockett derived a necessary condition for the existence of a feedback control law asymptotically stabilizing an equilibrium for a given nonlinear control system. The intuitive appeal and the ease with which it can be applied have made this criterion one of the standard tools in the study of the feedback stabilizability of nonlinear control systems. Brockett's original proof used an impressive combination of Liapunov theory and algebraic topology, in part to cope with a lacuna in our understanding of the topology of the sublevel sets of Liapunov functions. In [33], F. W. Wilson, Jr. extended the converse theorems of Liapunov theory to compact attractors and proved some fundamental results about the topology of their domain of attraction and the level sets of their Liapunov functions. In particular, Wilson showed that the level sets Mc = V −1 (c) are diffeomorphic to S n−1 for n = 4, 5 using the proof of the generalized Poincaré Conjecture of Smale. He observed that the excluded cases would from the validity of the Poincaré Conjecture in dimension 3 and 4 and showed that, for n = 5, the assertion ∂Mc ≃ S 4 would imply the Poincaré Conjecture for 4-manifolds. Of course, the topological Poincaré Conjecture for S 4 was subsequently proved by Freedman in 1980 and with the remarkable recent solution by Perelman of the classical Poincaré Conjecture, Wilson's Theorem now holds for all n. In this paper we describe the sublevel, and therefore as a corollary the level, sets of proper smooth functions V : R n → R having a compact set C(V) of critical points. Among the main results in this paper is the assertion that an arbitrary sublevel set Mc = V −1 [0, c] of such a function is homeomorphic to D n , the unit disk. For n = 2, this assertion is a consequence of the Schönflies Theorem, a classical enhancement of the Jordan Curve Theorem. For arbitrary n it follows from the generalized Schönflies Theorem of Mazur and Brown, from [33] and from the verification of the Poincaré Conjecture in all dimensions by Perelman, Freedman and Smale. We also describe the smooth structure of Mc and its boundary, generalizing the results of [33]. This result has several corollaries. In particular, using the Brouwer Fixed Point Theorem this gives a straightforward proof of Brockett's criterion and some of its enhancements to global attractors. These results in turn imply a new necessary condition for Input-to State Stability with respect to a compact set and an extension of Brockett's Theorem to the practical stabilizability of equilibria. Our main results can be further enhanced using the Poincaré-Hopf Theorem and, in this way, also lead to a streamlined version of Coron's proof [7] that Brockett's Theorem holds for continuous feedback laws, using a classical topological argument on the unit disc D n. 1. Introduction. Consider a control system (1.1)ẋ = f (x, u) x ∈ R n , u ∈ R m * Dedicated to my friend and teacher, Roger Ware Brockett, on the occasion of his seventieth birthday. Research supported in part by grants from the AFOSR.
Robustness to uncertain parameters of this popular induction motor controller is investigated. Co... more Robustness to uncertain parameters of this popular induction motor controller is investigated. Conditions for local and global asymptotic stability as well as boundedness of all signals are derived
Performance in an engineering system tends to degrade over time due to a variety of wearing or ag... more Performance in an engineering system tends to degrade over time due to a variety of wearing or ageing processes. In supervisory controlled processes there are typically many signals being monitored that may help to characterise performance degradation. It is preferred to select the least amount of information to obtain high quality of predictive analysis from a large amount of collected data, in which labelling the data is not always feasible. To this end a novel unsupervised feature selection method, robust with respect to significant measurement disturbances, is proposed using the notion of "weak monotonicity" (WM). The robustness of this notion makes it very attractive to identify the common trend in the presence of measurement noises and population variation from the collected data. Based on WM, a novel suitability indicator is proposed to evaluate the performance of each feature. This new indicator is then used to select the key features that contribute to the WM of a family of processes when noises and variations among processes exist. In order to evaluate the performance of the proposed framework of the WM and suitability, a comparative study with other nine state-of-the-arts unsupervised feature evaluation and selection methods is carried out on well-known benchmark datasets. The results show a promising performance of the proposed framework on unsupervised feature evaluation in the presence of measurement noises and population variations.
Despite the enormous benefit that has accrued to society from control technology and the continue... more Despite the enormous benefit that has accrued to society from control technology and the continued vitality of control science as a research field, there is broad consensus that the practitioners of control and the academic research community are insufficiently engaged with each other. We explore this concern with reference to the oft-cited theory/practice gap but also from an industry perspective. The core of this article is comprised of ten "messages," targeting primarily researchers interested in the practical impact of their work, that we hope shed insight on industry. Results from surveys and other data are cited to underpin the points. Some educational synergies between industry and academia are also noted. To highlight the continuing relevance of control science to industry, several recent examples of successful, deployed advanced control solutions are presented. The authors of this article are members of the IFAC Industry Committee, formally established in 2017 with objectives that include (per the updated IFAC Constitution) "increasing industry participation in and impact from IFAC activities."
Evaluating progress throughout a patient’s rehabilitation episode is critical for determining eff... more Evaluating progress throughout a patient’s rehabilitation episode is critical for determining effectiveness of the selected treatments and contributing to the evidence-based practice. The evaluation process is complex due to the inherent large human variations in motor recovery and the limitations of commonly used clinical measurement tools. Information recorded during a robot-assisted rehabilitation process can provide an effective means to continuously quantitatively assess movement performance and rehabilitation progress. However, selecting appropriate motion features for rehabilitation evaluation has always been challenging. This paper exploits unsupervised feature learning techniques to reduce the complexity of building the evaluation model of patients’ progress. A new feature learning technique is developed to select the most significant features from a large amount of kinematic features measured from robotics, providing clinically useful information to health practitioners wi...
Stability and performance of networked control systems has been a recent area of interest in the ... more Stability and performance of networked control systems has been a recent area of interest in the control literature. The inclusion of a shared communication network between plant and controller inevitably leads to occasional random data loss. We provide novel results relating to the probability of such a system being globally asymptotically stable or input to state stable.
Proceedings of the 15th IFAC World Congress, 2002, 2002
In this paper, an aircraft landing autopilot is designed using the nonlinear energybased control ... more In this paper, an aircraft landing autopilot is designed using the nonlinear energybased control method (NEM). This method provides the automatic landing by energy management idea. Using the NEM the stabilization and tracking can be achieved by modifying the energy functions. The method is illustrated on an automatic landing system problem for a twinengine civil aircraft, developed by Group for Aeronautical Research and Technology in Europe (GARTEUR). Further we provide physical interpretation of the control laws. A disturbance rejection and robustness analysis is also performed via numbers of simulations at extreme flight conditions. The proposed control laws behave well even under extreme flight conditions.
The stability of the signed regressor variant of least mean square (LMS) adaptation is found to b... more The stability of the signed regressor variant of least mean square (LMS) adaptation is found to be heavily dependent on the characteristics of the input sequence. Averaging theory is used to derive a persistence of excitation condition which guarantees exponential stability of the signed regressor algorithm. Failure to meet this condition (which is not equivalent to persistent excitation for LMS) can result in exponential instability, even with the use of leakage. This new persistence of excitation condition is then interpreted in both deterministic and stochastic settings.
A novel approach to finding an approximate analytic solution to the Bloch equation is developed i... more A novel approach to finding an approximate analytic solution to the Bloch equation is developed in this paper. The method is based on time scaling and averaging of the Bloch equation after transformation to a rotating frame of reference. In order to accomplish the scaling, a novel time scaled magnetisation vector is introduced. The resultant time scaled system is subsequently approximated through averaging, a technique that to the best of our knowledge, has not previously been applied in the nuclear magnetic resonance context. Our proposed method of approximating the solution to the Bloch equation is valid for continuous wave excitation as well as the traditional pulse excitation with an arbitrary envelope, making this a widely applicable technique unlike previously proposed methods. Comparison of the approximate analytic solution and simulation results clearly indicates that the error is negligible when the field inhomogeneities are small compared to the excitation field amplitude. Extremum seeking techniques may be applied to determine the optimal excitation, given the form of the approximate solution. This result is applicable to a range of research areas including nuclear magnetic resonance, magnetic resonance imaging and optical resonance problems.
Thr paper presents nonlinear averaging theorems lor two-time scale systems, where the dynamics of... more Thr paper presents nonlinear averaging theorems lor two-time scale systems, where the dynamics of the fast system are allowed to vary with the slow system. The results are &lied to the Narendra-Valavani adaplive canlrol algorithm, and estimates of the parameter convergence rates are obtained which d o not rely a n a linearization of the system around the cquilibriurn. and therciore arc valid in a larger region in the parameter space.
Output dead beat control for a class of non linear discrete time systems, which are described by ... more Output dead beat control for a class of non linear discrete time systems, which are described by a single input-output polynomial difference equation, is considered. The class of systems considered is restricted to systems with a two dimensional state space description. It is assumed that the highest degree with which the present input appears in the equation is odd. Necessary and sufficient conditions for the existence of output dead beat control and for the stability of the zero output constrained dynamics are presented. We also design a minimum time output dead beat control algorithm (feedback controller) which yields stable zero dynamics, whenever this is feasible. A number of interesting phenomena are discussed and illustrated by examples.
Mathematics of Control, Signals, and Systems, 1988
For continuous-time, multiple-input, multiple-output, linear systems, we present conditions under... more For continuous-time, multiple-input, multiple-output, linear systems, we present conditions under which the persistency of excitation of one regression vector implies the persistency of another regression vector derived from the first via a linear, dynamical transformation. We then introduce a definition of sufficient richness for vector input signals in the form of a persistency of excitation condition on a basis regression vector. Finally we establish input conditions which guarantee the persistency of excitation of a large class of regression vectors obtained from both time-invariant and time-varying systems.
Mathematics of Control, Signals, and Systems, 1997
We propose and analyse a populational version of stepwise gradient descent suitable for a wide ra... more We propose and analyse a populational version of stepwise gradient descent suitable for a wide range of learning problems. The algorithm is motivated by genetic algorithms which update a population of solutions rather than just a single representative a s i s t ypical for gradient descent. This modi cation of traditional gradient descent (as used for example in the backpropagation algorithm) avoids getting trapped in local minima. We use an averaging analysis of the algorithm to relate its behaviour to an associated ordinary di erential equation. We d e r i v e a result concerning how long one has to wait in order that with a given high probability, the algorithm is within a certain neighbourhood of the global minimum. We also analyse the e ect of di erent population sizes. An example is presented which corroborates our theory very well.
International Journal of Adaptive Control and Signal Processing, 1992
This paper addresses certain functional learning tasks in signal processing using familiar algori... more This paper addresses certain functional learning tasks in signal processing using familiar algorithms and analytical tools of least squares for autoregressive moving average exogonous input (ARM AX) models. The models can be viewed as conventional ARM AX models but with parameters dependent on variables such as inputs or states. termed function input variables. The functional dependence of the parameters on these variables is represented in terms of basis function expansions, or more generaliv int erpoiation function representations. The interpolation functions in a least squares identification of coefficients also turn out to be in essence spread functions that spread learning throughout the space of function input variables. Thus for a set of training sequences. or trajectories in function input space, system parameters and thereby system functional can be updated. The idea is that these will have relevance for similar sequences or neighboring trajectories. The concept of persistence of excitation to achieve complete function learning, or equivalently, signal model learning is studied using least squares convergence results. Application of the proposed algorithms and theory within the signal processing context is addressed by means of simple illustrative examples. q Work partially supported by Boeing (BCAC).
In this paper, we address the problem of reduced-complexity estimation of general large-scale hid... more In this paper, we address the problem of reduced-complexity estimation of general large-scale hidden Markov models (HMMs) with underlying nearly completely decomposable discrete-time Markov chains and finite-state outputs. An algorithm is presented that computes () (where is the related weak coupling parameter) approximations to the aggregate and full-order filtered estimates with substantial computational savings. These savings are shown to be quite large when the chains have blocks with small individual dimensions. Some simulation studies are presented to demonstrate the performance of the algorithm.
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1997
In the literature on dynamical systems analysis and the control of systems with complex behavior,... more In the literature on dynamical systems analysis and the control of systems with complex behavior, the topic of synchronization of the response of systems has received considerable attention. This concept is revisited in the light of the classical notion of observers from (non)linear control theory.
Dead-beat controllers for simple Hammerstein systems are investigated. Several designs for nonmin... more Dead-beat controllers for simple Hammerstein systems are investigated. Several designs for nonminimum-time state dead-beat controllers are given for certain classes of simple Hammerstein systems. A general minimum-time state dead-beat controller is presented for a class of simple Hammerstein systems. A design for a family of minimum-time control laws is provided. This enables, to a certain extent, shaping of transient response via choosing an appropriate control law. Finally, the authors design an output dead-beat controller for a class of Hammerstein systems that are not necessarily state dead-beat controllable.
Output deadbeat control in one step is considered for a class of discrete-time systems described ... more Output deadbeat control in one step is considered for a class of discrete-time systems described by a nonlinear single-input/singleoutput recursive representation. Global stability conditions are established for the particular subclass of systems with one-dimensional zero dynamics. The results are illustrated with applications to polynomial and neural dynamical systems.
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Papers by Iven Mareels