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Affine Systems (affine + system)

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Engineering100%

Selected Abstracts

SINGULARITY COMPUTATION FOR ITERATIVE CONTROL OF NONLINEAR AFFINE SYSTEMS

ASIAN JOURNAL OF CONTROL, Issue 2 2000
Dan O. Popa
ABSTRACT This paper considers a gradient type of iterative algorithm applied to the open loop control for nonlinear affine systems. The convergence of the algorithm relies on the control signal in each iteration be nonsingular. We present an algorithm for computing the singular control for a general class of nonlinear affine systems. Various nonlinear mechanical systems, including nonholonomic systems, are included as examples. [source]

Global robust stabilization of nonlinear systems subject to input constraints

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2002
Rodolfo Suárez
Abstract Our main purpose in this paper is to further address the global stabilization problem for affine systems by means of bounded feedback control functions, taking into account a large class of control value sets: p,r -weighted balls ,mr(p), with 10 are also considered. Working along the line of Artstein,Sontag's approach, we construct an explicit formula for a one-parameterized family of continuous feedback controls taking values in ,rm(p) that globally asymptotically stabilize an affine system, provided an appropriate control Lyapunov function is known. The designed family of controls is suboptimal with respect to the robust stability margin for uncertain systems. The problem of achieving disturbance attenuation for persistent disturbances is also considered. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Inf,sup control of discontinuous piecewise affine systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2009
J. Spjřtvold
Abstract This paper considers the worst-case optimal control of discontinuous piecewise affine (PWA) systems, which are subjected to constraints and disturbances. We seek to pre-compute, via dynamic programming, an explicit control law for these systems when a PWA cost function is utilized. One difficulty with this problem class is that, even for initial states for which the value function of the optimal control problem is finite, there might not exist a control law that attains the infimum. Hence, we propose a method that is guaranteed to obtain a sub-optimal solution, and where the degree of sub-optimality can be specified a priori. This is achieved by approximating the underlying sub-problems with a parametric piecewise linear program. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Stability analysis and guaranteed domain of attraction for a class of hybrid systems: an LMI approach

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2003
S. Palomino Bean
Abstract This paper presents sufficient conditions for the regional stability problem for switched piecewise affine systems, a special class of Hybrid Systems. This class of systems are described by an affine differential equation of the type x,=A(,)x+b(,), where x denotes the continuous state vector and , is a vector of logical variables that modifies the local model of the system in accordance with the continuous dynamics. Using a Lyapunov function of the type v(x)=x,P(x)x, we present LMI conditions that, when feasible, guarantee local stability of the origin of the switched system. Examples of switched affine systems are used to illustrate the results. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Robust adaptive fuzzy controller for non-affine nonlinear systems with dynamic rule activation

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2 2003
Jang-Hyun Park
Abstract This paper describes the design of a robust adaptive fuzzy controller for an uncertain single-input single-output nonlinear dynamical systems. While most recent results on fuzzy controllers considers affine systems with fixed rule-base fuzzy systems, we propose a control scheme for non-affine nonlinear systems and a dynamic fuzzy rule activation scheme in which an appropriate number of the fuzzy rules are chosen on-line. By using the proposed scheme, we can reduce the computation time, storage space, and dynamic order of the adaptive fuzzy system without significant performance degradation. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as for all other signals in the closed loop. No a priori knowledge of an upper bounds on the uncertainties is required. The theoretical results are illustrated through a simulation example. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Global robust stabilization of nonlinear systems subject to input constraints

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2002
Rodolfo Suárez
Abstract Our main purpose in this paper is to further address the global stabilization problem for affine systems by means of bounded feedback control functions, taking into account a large class of control value sets: p,r -weighted balls ,mr(p), with 10 are also considered. Working along the line of Artstein,Sontag's approach, we construct an explicit formula for a one-parameterized family of continuous feedback controls taking values in ,rm(p) that globally asymptotically stabilize an affine system, provided an appropriate control Lyapunov function is known. The designed family of controls is suboptimal with respect to the robust stability margin for uncertain systems. The problem of achieving disturbance attenuation for persistent disturbances is also considered. Copyright © 2002 John Wiley & Sons, Ltd. [source]

H, control for nonlinear affine systems: a chain-scattering matrix description approach

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2001
Jang-Lee Hong
Abstract This paper combines an alternative chain-scattering matrix description with (J, J,)-lossless and a class of conjugate (,J, ,J,)-lossless systems to design a family of nonlinear H, output feedback controllers. The present systems introduce a new chain-scattering setting, which not only offers a clearer expression for the solving process of the nonlinear H, control problem but also removes the fictitious signals introduced by the traditional chain-scattering approach. The intricate nonlinear affine control problem thus can be transformed into a simple lossless network and is easy to deal with in a network-theory context. The relationship among these (J, J,) systems, L2 -gain, and Hamilton,Jacobi equations is also given. Block diagrams are used to illustrate the central theme. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Observer-based controller design of discrete-time piecewise affine systems

ASIAN JOURNAL OF CONTROL, Issue 4 2010
Ya-Hui Gao
Abstract This paper presents a novel observer-based controller design method for discrete-time piecewise affine (PWA) systems. The basic idea is as follows: at first, a piecewise linear (without affine terms) state feedback controller and a PWA observer are designed separately, and then it is proved that the output feedback controller constructed by the resulting observer and state feedback controller gains can guarantee the stability of the closed-loop system. During the controller design, the piecewise-quadratic Lyapunov function technique is used. Moreover, the region information is taken into account to treat the affine terms, so the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically feasible with commercially available software. Three simulation examples are given finally to verify the proposed theoretical results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

SINGULARITY COMPUTATION FOR ITERATIVE CONTROL OF NONLINEAR AFFINE SYSTEMS

ASIAN JOURNAL OF CONTROL, Issue 2 2000
Dan O. Popa
ABSTRACT This paper considers a gradient type of iterative algorithm applied to the open loop control for nonlinear affine systems. The convergence of the algorithm relies on the control signal in each iteration be nonsingular. We present an algorithm for computing the singular control for a general class of nonlinear affine systems. Various nonlinear mechanical systems, including nonholonomic systems, are included as examples. [source]