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55
An analysis and design method for linear systems subject to actuator saturation and disturbance
, 2002
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Global analysis of piecewise linear systems using impact maps and quadratic surface Lyapunov functions: general theory. Submited for publication
 IEEE Transactions on Automatic Control
"... analysis, switching surfaces. In this paper we develop an entirely new constructive global analysis methodology for a class of hybrid systems known as Piecewise Linear Systems (PLS). This methodology consists in inferring global properties of PLS solely by studying their behavior at switching surfac ..."
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Cited by 27 (3 self)
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analysis, switching surfaces. In this paper we develop an entirely new constructive global analysis methodology for a class of hybrid systems known as Piecewise Linear Systems (PLS). This methodology consists in inferring global properties of PLS solely by studying their behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface, by constructing quadratic Lyapunov functions on switching surfaces. We found that an impact map induced by an LTI flow between two switching surfaces can be represented as a linear transformation analytically parameterized by a scalar function of the state. This representation of impact maps allows the search for quadratic surface Lyapunov functions to be done by simply solving a set of LMIs. Global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS can this way be efficiently checked. These new results were successfully applied to certain classes of PLS. Although this analysis methodology yields only sufficient criteria of stability, it has shown to be very successful in globally analyzing a large number of examples with a locally stable limit cycle or equilibrium point. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. 1
Antiwindup design: an overview of some recent advances and open problems
, 2007
"... This paper deals with the antiwindup technique which can be used to tackle the problems of stability and performance degradation for linear systems with saturated inputs. The antiwindup techniques which can be found in the literature today have evolved from many sources and, even now, are diverse ..."
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Cited by 27 (2 self)
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This paper deals with the antiwindup technique which can be used to tackle the problems of stability and performance degradation for linear systems with saturated inputs. The antiwindup techniques which can be found in the literature today have evolved from many sources and, even now, are diverse and somewhat disconnected from one another. In this survey, an overview of many recent antiwindup techniques are provided and their connections to one another are stated. The antiwindup technique is also explained within the context of its historical emergence and the likely future directions of the field are speculated. The focus of this paper is on the socalled “modern” antiwindup techniques which began to emerge during the end of the 20th century and which allow a priori guarantees on stability to be made. The survey attempts to provide constructive LMI conditions for the synthesis of antiwindup compensators in both global and local contexts. Finally, some interesting extensions and open problems are discussed, such as nested saturations, the presence of time delays in the state or the input, and antiwindup for nonlinear systems.
Highgain observers in nonlinear feedback control
 INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
, 2013
"... In this document, we present the main ideas and results concerning highgain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating secondorder example is used to illustrate the key features of highgain observers and their use i ..."
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Cited by 22 (1 self)
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In this document, we present the main ideas and results concerning highgain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating secondorder example is used to illustrate the key features of highgain observers and their use in feedback control. This is followed by a general presentation of highgainobserver theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of highgain observers in the robust control of minimumphase nonlinear systems.
NeuralNetworkBased NearOptimal Control for a Class of DiscreteTime Affine Nonlinear Systems With Control Constraints
"... Abstract—In this paper, the nearoptimal control problem for a class of nonlinear discretetime systems with control constraints is solved by iterative adaptive dynamic programming algorithm. First, a novel nonquadratic performance functional is introduced to overcome the control constraints, and th ..."
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Cited by 22 (6 self)
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Abstract—In this paper, the nearoptimal control problem for a class of nonlinear discretetime systems with control constraints is solved by iterative adaptive dynamic programming algorithm. First, a novel nonquadratic performance functional is introduced to overcome the control constraints, and then an iterative adaptive dynamic programming algorithm is developed to solve the optimal feedback control problem of the original constrained system with convergence analysis. In the present control scheme, there are three neural networks used as parametric structures for facilitating the implementation of the iterative algorithm. Two examples are given to demonstrate the convergence and feasibility of the proposed optimal control scheme. Index Terms—Adaptive dynamic programming, approximate dynamic programming, control constraints, convergence analysis, nearoptimal control, neural networks. I.
LowandHigh Gain Design Technique for Linear Systems Subject to Input Saturation  A Direct Eigenstructure Assignment Approach
 International Journal of Robust and Nonlinear Control
, 1994
"... The lowandhigh gain design technique, which was initiated in [10] for a chain of integrators and completed in [13] for general linear asymptotically null controllable with bounded controls systems, was conceived for semiglobal control problems beyond stabilization and was related to the performan ..."
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Cited by 19 (9 self)
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The lowandhigh gain design technique, which was initiated in [10] for a chain of integrators and completed in [13] for general linear asymptotically null controllable with bounded controls systems, was conceived for semiglobal control problems beyond stabilization and was related to the performance issues such as semiglobal stabilization with enhanced utilization of the available control capacity and semiglobal disturbance rejection. Although the lowandhigh gain design technique as initiated in [10] is based on explicit eigenstructure assignment, its full development in [13] is based on the solution of an algebraic Riccati equation (ARE) which is parameterized in an arbitrarily small scalar, called low gain parameter. In this paper, we develop a new complete lowand high gain design procedure which is based on explicit eigenstructure assignment. The new design approach avoids the solution of the numerically stiff parameterized ARE. Submitted to International Journal of Robust an...
SemiGlobal Stabilization of Linear DiscreteTime Systems Subject to Input Saturation via Linear Feedback  An AREBased Approach
, 1996
"... We revisit the problem of semiglobal stabilization of linear discretetime systems subject to input saturation and give an algebraic Riccati equation (ARE)based approach to the proof of a fact we established earlier ([?]), i.e., a linear discretetime system subject to input saturation is semiglo ..."
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Cited by 15 (2 self)
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We revisit the problem of semiglobal stabilization of linear discretetime systems subject to input saturation and give an algebraic Riccati equation (ARE)based approach to the proof of a fact we established earlier ([?]), i.e., a linear discretetime system subject to input saturation is semiglobally stabilizable via linear feedback as long as the linear system in the absence of the saturation is stabilizable and detectable and all its open loop poles are located inside or on the unit circle. Moreover, we drastically relax the requirements on the characteristic of the saturation elements as imposed in our earlier work [?]. 1 1. Introduction In this paper we revisit the problem of stabilizing a general linear system which is subject to input saturation. Over the last few years, there has been rather strong interest in this problem, possibly due to a wide recognition of the inherent constraints on the control input. As a result, several important results have appeared in the open ...
SLQR/SLQG: An LQR/LQG Theory for Systems with Saturating Actuators
 CGR0003, EECS, UNIVERSITY OFMICHIGAN, ANN ARBOR
, 2000
"... An extension of the LQR/LQG methodology to systems with saturating actuators, referred to as SLQR/SLQG, is obtained. The development is based on the method of stochastic linearization. Using this method and the Lagrange multiplier technique, solutions to the SLQR and SLQG problems are derived. These ..."
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Cited by 8 (0 self)
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An extension of the LQR/LQG methodology to systems with saturating actuators, referred to as SLQR/SLQG, is obtained. The development is based on the method of stochastic linearization. Using this method and the Lagrange multiplier technique, solutions to the SLQR and SLQG problems are derived. These solutions are given by Riccati and Lyapunov equations coupled with two transcendental equations. It is shown that, under standard stabilizability and detectability conditions, these equations have a unique solution, which can be found by a simple bisection algorithm. When the level of saturation tends to infinity, these equations reduce to their standard LQR/LQG counterparts.
Any Domain of Attraction for a Linear Constrained System is a Tracking Domain of Attraction
, 2000
"... We face the problem of determining a tracking domain of attraction, say the set of initial states starting from which it is possible to track reference signals in given class, for discretetime systems with control and state constraints. We show that the tracking domain of attraction is exactly equa ..."
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Cited by 6 (1 self)
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We face the problem of determining a tracking domain of attraction, say the set of initial states starting from which it is possible to track reference signals in given class, for discretetime systems with control and state constraints. We show that the tracking domain of attraction is exactly equal to the domain of attraction, say the set of states which can be brought to the origin by a proper feedback law. For constant reference signals we establish a connection between the convergence speed of the stabilization problem and tracking convergence which turns out to be independent of the reference signal. We also show that the tracking controller can be inferred from the stabilizing (possibly nonlinear) controller associated with the domain of attraction. We refer the reader to the full version [17], where the continuoustime case, proofs and extensions are presented. 1 Introduction We consider linear systems with state and control constraints and we say that a certain convex and co...
Global stabilization of a class of uncertain systems with saturated adaptive robust control
 IEEE Conf. on Decision and Control
, 2000
"... In this paper, a class of saturated adaptive robust control (SARC) laws are developed for nonlinear systems in the \chainofintegrator " form with both parametric uncertainties and nonrepeatable uncertainties. A guaranteed transient performance and nal tracking accuracy is achieved in gene ..."
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Cited by 5 (2 self)
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In this paper, a class of saturated adaptive robust control (SARC) laws are developed for nonlinear systems in the \chainofintegrator " form with both parametric uncertainties and nonrepeatable uncertainties. A guaranteed transient performance and nal tracking accuracy is achieved in general. Furthermore, asymptotic output tracking is also achievable provided that the system undergoes parametric uncertainties only. Discontinuous projection method is used in the adaptation law for a controlled learning. Given the saturation limits of control authority, certain criteria are obtained to predict the achievable highperformance working range of the closedloop system by taking into account the order of system, the bounds of both parametric uncertainties and nonrepeatable nonlinearities, and the required performance, such as reaching time. At the same time, these criteria can also be used in the trajectory planning to obtain realizable desired trajectories. Consequently, an integrated design of achievable desired trajectory and control law may be achieved. The proposed SARC is then applied to the control of a linear motor drive system, and an excellent output tracking performance is obtained in experiments. 1