Discrete Descriptor Systems Research Articles

Dual linear quadratic optimal control for two-point boundary value descriptor systems

The dual linear quadratic opiimal control problem for the two-point boundary value case of discrete descriptor systems is investigated. It is shown that, in the case where the cost functional docs not have cross terms, the optimal control law can be expressed as an affine function of the stale of the non-causal subsystem, while the optimal cost-to-go can be expressed as a general quadratic expression of the state of the non-causal subsystem.

Open-Loop Linear Quadratic Nash Games for Discrete Descriptor Systems

This paper is concerned with the computation of Nash solutions for a class of deterministic linear-quadratic two-person nonzerosum difference games. The dynamics of the system is characterized by a linear discretetime descriptor equation Exk+1=Axk+Buk+Cvk, where E is singular. The games are studied under the open-loop information structure. It is proven that the linear quadratic Nash game of the discrete descriptor system always admit uncountable Nash equilibrium solutions even if the information structure of the game is open-loop. This property is very different from that in the open-loop Nash game of a state space system. A pair of minimum-norm open-loop Nash solutions is computed by recursively solving two coupled asymmetric Riccati-type matrix equations.

Deadbeat control of discrete descriptor systems with inaccessible descriptor vector

The problem of deadbeat compensator design is considered for a discrete descriptor system with inaccessible descriptor variables. The full compensator design is reduced to separate designs of two regular deadbeat controllers of a lower order. Driven by this compensator, the descriptor variables of the system, starting from given initial conditions, can reach the origin in a minimum of μc + μ0 time steps, where μc and μc are the largest right Kronecker indices of the pencils [zE − A B] and [zE − A′ C′], respectively.

L-Q optimal control for discrete descriptor systems with a complete set of boundary information

This paper presents the linear-quadratic optimal control problem for the discrete-time descriptor systems Exk+1 = Axk + Buk, where E is a singular matrix, the system structure is, in general, non-causal and its boundary conditions information is specified in terms of d initial conditions and (n – d) final conditions, where d = deg {det (λE – A)}. It is shown that the optimal control law depends only on the d-dimensional state variables of the causal subsystem, and the optimal cost-to-go is a general quadratic expression of the causal state variables and does not depend on the entire descriptor vector. This result constitutes an extension to the non-causal system case of Larson et al. (1978), where the structure of the descriptor system had been assumed causal.

Fundamental, reachability, and observability matrices for discrete descriptor systems

This paper uses the fundamental matrix of a regular discrete descriptor system to derive expressions for descriptor reachability and observability matrices. Reachable and unobservable subspaces are defined. It is shown that the natural space for analyzing descriptor system properties is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R^{2n}</tex> (where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> is the dimension of the system), not R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> as is the case for state-space systems. Solutions are provided for the descriptor open-loop control and estimation problems.