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Exact determinantions of maximal output admissible set for a class of semilinear discrete systems

El Bhih Amine, Benfatah Youssef, Rachik Mostafa

Archives of Control Sciences

2020

Vol. 30, No. 3

523--552

Consider the semilinear system defined by {x(i+1)=Ax(i)+f(x(i)), i≥0 x(0)=x0∈Rn and the corresponding output signal y(i)=C x(i), i≥0, where A is a n×n matrix, C is a p x n matrix and f is a nonlinear function. An initial state x(0) is output admissible with respect to A, f, C and a constraint set Ω ⊂ Rp, if the output signal (y(i)i associated to our system satisfies the condition y(i) ∈ Ω, for every integer i≥0. The set of all possible such initial conditions is the maximal output admissible set Γ(Ω). In this paper we will define a new set that characterizes the maximal output set in various systems(controlled and uncontrolled systems) .Therefore, we propose an algorithmic approach that permits to verify if such set is ﬁnitely determined or not. The case of discrete delayed systems is taken into consideration as well. To illustrate our work, we give various numerical simulations.

Guaranteed control policy with arbitrary set of correction points for linear-quadratic system with delay

Chong K. T., Kostyukova O., Kurdina M.

Control and Cybernetics

2010

Vol. 39, no 3

739-768

For continuous, uncertain, linear quadratic control system with delayed input, we consider a min-max control policy in which the elements of feedback are present. The feedback is introduced into control optimization by allowing a control to be corrected at a given set of correction points from the control interval. This helps to overcome the feasibility difficulties that arise with standard min-max techniques. We show that construction of the optimal policy involves a sequence of min-max optimizations formulated as dynamic programs that do not yield simple analytical solutions. That is why the paper is mainly focused on construction and justification of suboptimal control policy that can be effectively implemented. Simulated examples demonstrate the proposed approach.