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Let A0 be a possibly unbounded positive operator on the Hilbert space H, which is boundedly invertible. Let C0 be a bounded operator from D(A1/20) (with the norm ||z||21/2 = 〈A0z, z〉) to another Hilbert space U. It is known that the system of equations z(t) + A0 z(t) + 1/2 C∗0 C0 Z(t) = C∗0u(t), y(t) = − C0 z(t) + u(t), determines a well-posed linear system Σ with input u and output y, input and output...
In this note we study the robustness of Generalized PI (GPI) control with respect to parametric uncertainties. We present two cases of study: a second order linear system and the inertia wheel pendulum. We propose a step by step procedure which may be used in each particular application.
It is shown that a nonlinear continuous-time control system with output is externally dynamically linearizable if and only if its differential output universe is free. Some regularity conditions are assumed, but the system does not have to be observable. Using universes instead of algebras or fields is essential as they allow for substitutions and amalgamations of functions.
We develop the study of primitives of human motion, which we refer to as movemes. The idea is to understand human motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet of dynamical systems. How can we construct an alphabet of movemes from human data? In this paper we address this issue by introducing the notion of well-posednes. Using examples from...
Synthesis of static anti-windup compensators is considered. LMI conditions are established for stability and performance analysis of the closed loop system. The performance criterion describes the servo problem for the resulting closed-loop piece-wise linear system. The synthesis of the anti-windup compensators will be given by some bilinear matrix inequalities.
The robustness of discrete iterative learning controller a-gainst initial state state error for discrete-time plant is investigated in this paper. When the initial state remains fixed for each iteration but is different from the desired one, it is shown that the output will converge to a trajectory which is the same as the desired one except the initial point for a traditional D-type discrete iterative...
This paper addresses the problem of state reduction of nonlinear continuous-time systems. A novel method that relates to balanced truncation is presented and applied to examples. The method is computationally efficient and is applicable to relatively large systems.
The concept of algebraic reachability refers to the property of a system that every state from a sufficiently big subset of a state-space can be reached from a given inital state by applying an admissible input to the system. In this paper we study algebraic reachability of rational systems. We provide necessary and sufficient conditions for a rational system to be algebraically reachable (from an...
The paper presents new observability and detectability concepts for continuous-time Markov jump linear systems with finite Markov state, which generalize previous corresponding concepts found in the literature. The concept can also assure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is unique and stabilizing, making other concepts redundant...
We deal with linear systems with Markovian Jump Parameters (LSMJP). Most of the literature on this matter adopts a finite state space for the Markov chain. In this paper we focus on the countably infinite state space case showing that, unlike the finite state space case (see [8]), two important concepts in optimal control theory, namely, stochastic stability (SS) and mean square stability (MSS) are...
We show that a delay-differential system, i.e. a dynamical system that is defined by a set of equations involving differentiation and both punctual and distributed delays, can be written in a pseudo-state space form, called also first- order representation, which generalizes the state space form for purely differential systems and employs only first-order derivatives and punctual delays.
In this paper we present a sufficient condition for global observability of nonlinear systems on manifolds that generalizes Aeyels' global observability result for Morse-Smale systems. Our main theorem establishes global observability under considerably weaker assumptions than Aeyels' Morse-Smale condition. However, we have to assume additionally real analyticity of the system. With this result at...
In this paper, the problem of the determination of the maximal controlled invariant set of linear systems subject to polyhedral input and state constraints, together with the corresponding state-feedback control law is investigated. Instead of computing one-step reachable sets or maximizing the volume of a specific invariant set, the proposed method consists of the iterative expansion of an initial...
We use the behavioural approach to provide definitions and characterisations of invariant zeros of nD systems. In particular we show that the definitions are equivalent in the 1D case to those in the classical literature. We provide new results on the structural relations of nD invariant and transmission zeros.
In this paper we consider a formulation of the H2 optimal control problem in which the controller is not viewed as an operator that transforms measurements to controls. Instead, the controller is assumed to be a device that constrains a set of a-priori specified interconnection variables so as to achieve a controlled system whose manifest variables have a free component and satisfy an upperbound on...
In this paper, we provide the complete solution to the reconfigurable control problem after actuator faults in linear dynamical systems by means of disturbance decoupling approaches. The recovery of the closed-loop internal stability and the exact and approximate recovery of nominal tracking and performance are our main reconfiguration goals. We state necessary and sufficient conditions for the solvability...
We consider here the problem of finding a controller for a system such that when interconnected to the plant, we get a system which is bisimilar to the desired system. We give necessary and sufficient conditions for the existence of such a controller. The systems we consider are ordinary linear time invariant dynamical systems described by state space equations. We briefly compare our results with...
This paper presents a new adaptive nonlinear control for trajectory tracking of non-affine nonlinear systems. The referred proposed controller which is based on a L2 norm prescribed to minimize a trajectory tracking error has adaptive and optimal characters. Moreover with the systems output feedback, the proposed controller which dose not require any knowledge of nonlinear internal dynamics can be...
We consider the problem of controlling plants that are subject to multiple saturation constraints. Especially, we are interested in linear systems whose input is subject to amplitude and rate constraints of saturation type. Furthermore, the considered systems output is also subject to an intrinsic saturation. Then, aiming to design global (and asymptotic) output tracking of compatible output-reference...
This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP that decomposes into small independent subproblems. We test the decomposition algorithm using a simple power management...
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