Discrete‐time sector based hands‐off control for nonlinear system

Abstract

Summary This article presents a hands‐off control design for discrete‐time nonlinear system with a special type of nonlinear sector termed as “discrete‐time [𝒦,𝒦ℒ] sector.” The design method to define the boundary of a discrete‐time [𝒦,𝒦ℒ] sector is done with control‐Lyapunov function. The generalization of nonlinear system is viewed in the perspective of a comparison function. By means of a proposed sector, a switching control is designed such that no control action is experienced inside the sector thus, saving unnecessary control efforts. However, to study the robustness for discrete‐time system, a hands‐off control is modified to ensure the monotonic decrease in the energy of the system. Finally, the proposed approach is verified with the simulation results.

Quantized‐feedback hands‐off control for nonlinear systems

“…Therefore, by combining ( 23) and ( 28), we can make the statement that the inequality (21) is obtained. This completes the proof.…”

“…Using the same idea, a continuous‐time sector is designed in [20] where the states monotonically decrease towards the origin. Moreover, the same idea is exploited for the discrete‐time sector [21], robust ] sector [22], and continuous‐time sector in the presence of disturbance [23]. In addition to this, some of the robust control techniques for the stabilization of nonlinear system has been explained in [24–29].…”

Design of Sparse Control With Minimax Concave Penalty

“…Due to these benefits, sparse control is often referred to as green control [5]. Theoretical results on sparse control have been actively reported for various systems, including stochastic control systems [6], infinite-dimensional systems [7], discretetime linear systems [8]- [10], and nonlinear systems [11], [12]. Additionally, applications in diverse fields have been proposed, such as thermally activated building systems (TABS) [13], mobility networks [14], quadrotors [15], spacecrafts [16]- [18], and robotics [19].…”

Time‐optimal L1/L2 norms optimal control for linear time‐invariant systems

“…The time‐optimal sparse control with multiple sparsity measures 17 was solved by a sequential linear programming algorithm. The sparse optimal control design 18 for discrete‐time nonlinear systems with a special type of nonlinear sector termed was proposed and the robustness of the discrete‐time system was proved. The optimization problem enhancing the sparsity has not only been fully studied in linear time‐invariant systems but also in partial differential equation systems.…”