access icon free Stochastic LQ control under asymptotic tracking for discrete systems over multiple lossy channels

This study addresses the asymptotic tracking problem subjected to linear quadratic (LQ) constraints for linear discrete-time systems, where packet dropout occurs in actuating channels. To solve this objective control problem, the controller-coding co-design approach is adopted, i.e. the controller, encoder and decoder are designed for taking full advantage of the network resource collaboratively, thereby achieving better transmission of control signals. A stabilisability condition in the mean square sense that reveals the fundamental limitation among the norm of the plant, data arrival rates and coding matrices is first derived. Then, a solvability condition is conducted to handle the additional stochastic LQ control objective by a modified discrete-time algebraic Riccati equation, and an iterative algorithm is also given for designing the corresponding state feedback gain and coding matrices. Relied on such design, the asymptotic tracking constraint is further fulfilled through solving a Sylvester equation, and the feedforward gain related to tracking is parameterised. Finally, a simulation with the implementation of the design method on two cooperative robots is included to show the effectiveness of the current results.

Inspec keywords: linear systems; feedforward; Riccati equations; control system synthesis; matrix algebra; state feedback; discrete systems; stochastic systems; iterative methods; linear quadratic control; discrete time systems

Other keywords: linear discrete-time systems; control signals; mean square sense; additional stochastic LQ control objective; stabilisability condition; fundamental limitation; packet dropout; actuating channels; network resource; discrete systems; design method; objective control problem; multiple lossy channels; decoder; corresponding state feedback gain; solvability condition; data arrival rates; controller-coding co-design approach; coding matrices; asymptotic tracking problem; encoder; modified discrete-time algebraic Riccati equation; linear quadratic constraints; asymptotic tracking constraint

Subjects: Discrete control systems; Other topics in statistics; Stability in control theory; Control system analysis and synthesis methods; Optimisation techniques; Linear control systems; Interpolation and function approximation (numerical analysis); Optimal control; Algebra

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