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In this paper we consider an alternative approach to implementing Model Predictive Control (MPC). We show that solving a class of quadratic programming (QP) problems is equivalent to solving a class of well-posed nonlinear algebraic loops. These algebraic loops are closely related to that found in static anti-windup synthesis. It therefore follows that certain classes of MPC can be implemented in...
This paper addresses the problem of the determination of regions of stability for linear systems with amplitude and successive dynamics restricted actuator through anti-windup strategies. The objective by designing anti-windup gains is to guarantee the stability of the closed-loop system and the respect of the controlled output constraints for a region of admissible initial states as large as possible...
Predictive switching logic schemes are considered whereby a feedback-gain is switched-on at any time from a bank of candidate feedback-gains so as to control a discrete-time input-saturated LTI system possibly subject to persistent bounded disturbances of unknown arbitrary magnitude. It is constructively shown that such schemes do exist which ensure, along with good tracking performance, global asymptotic...
A general framework for designing antiwindup control systems is developed. More traditional anti-windup schemes generally suffer from several limitations, including the lack of (a priori) robustness respect to plant uncertainty, and also have a considerable heuristic component. The design method proposed in this paper provides an accurate graphic design procedure that guarantees closed loop global...
This paper considers H2 controllers implemented using an explicit observer for systems subjected to input magnitude saturation. It is stressed that the approach of only focusing on controller windup, by using fundamental observer anti-windup technique where the observer is fed by the saturated control signal, could imply severely deteriorated closed-loop characteristics and even sustained oscillations.
In this paper it is shown that under certain conditions the explicit model-based tracking optimal control law for constrained input linear dynamic systems results in the same control actions as a certain class of anti-windup control design techniques. This work clearly demonstrates how parametric programming transforms systematically the complex model-based advanced control technology to a simple...
In this paper, the robust stabilization problem for a class of nonlinear uncertain systems is studied using sliding mode techniques. Matched and mismatched uncertainties are both considered. By employing the sliding surface proposed by Zak and Hui [7], the stability of the sliding mode is shown first. Then, an asymptotic observer is established to estimate the system state variables based on a constrained...
A 2-sliding algorithm to stabilise a class of nonlinear systems of relative degree two with respect to the input is presented. It does not require the output derivative to be measured or observed.
In this note we combine a descriptor approach to stability and control of linear systems with time-varying delays, which is based on the Lyapunov — Krasovskii techniques, with a recent result on sliding mode control of such systems. The systems under consideration have norm-bounded uncertainties and uncertain bounded delays. The solution is given in terms of linear matrix inequalities (LMIs) and improves...
Sliding mode control synthesis is developed for a class of nonlinear time-delay systems. The corresponding free-delay system is assumed to be controllable whereas no stability assumptions are imposed on the open-loop system. The synthesis is based on a new delay-dependent stability criterion. The controller constructed proves to be robust against sufficiently small delay variations and external disturbances...
This paper deals with the combination of sliding mode control (SMC) and fuzzy logic system (FLS) for a class of non-linear multi-input multi-output (MIMO) uncertain systems. An adaptive scheme for the fuzzy control is developed to approximate the unknown system functions. A SMC is then applied to reduce the effects of both approximation errors and external disturbances. Thanks to Lyapunov's theory,...
This paper applies the decomposition block control technique to design a discontinuous regulator that guarantees asymptotic reference tracking for a class of linear delayed systems with disturbances. This class of systems is those presented in so-called Block Controllable Form with Delay. The block control technique is used to derive a sliding manifold on which the motion of the closed-loop system...
In this paper, we propose a necessary and sufficient condition for incremental stability of the interconnection of an LTI system with a static nonlinearity. The complexity of the condition is discussed.
A novel technique for synthesizing dynamic state feedback controllers that achieve practical input to state stability (PISS) property for nonlinear discrete-time systems is presented. The PISS controller design for the original system is solved via an auxiliary l∞-bounded (LIB) robustness synthesis problem for an auxiliary system. A complete solution for the LIB synthesis problem has been presented...
This paper is concerned with the local stability of a piece-wise affine system. In terms of piecewise quadratic Lyapunov functions, we derive a new matrix inequality condition that explicitly characterizes an inner approximation of the domain of attraction for the piecewise affine system. We also show the effectiveness of the present method by two numerical examples.
The purpose of this paper is to show how the theory of fractional ideals is a powerful mathematical framework for the study of stabilization problems of linear SISO systems. In particular, in terms of fractional ideals, we give necessary and sufficient conditions for a plant to be internally/strongly/bistably stabilizable or to admit a (weakly) coprime factorization. Finally, we show how to extend...
The explicit determination of the largest admissable constant controller is difficult. For linear systems with all poles in the domain of stability but at least one zero outside, an improved upper bound on real proportional gain controllers is given. An example shows the improvement and further possible margins.
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