Stabilization of Nonlinear Control-Affine Systems With Multiple State Constraints

Abstract

This paper considers the synthesis of stabilizing controllers for nonlinear control-affine systems under multiple state constraints. A new control Lyapunov-barrier function approach is introduced for solving the considered problem. Assuming a classical control Lyapunov function, two possible methods for constructing new control Lyapunov-barrier functions are discussed. Sufficient conditions for the existence of new control Lyapunov-barrier functions are derived. With modifying the Sontag's formula, an explicit stateconstrained stabilizing feedback law is presented. Finally, two numerical examples are provided to illustrate the obtained theoretical results.

Design of Event-Triggered State-Constrained Stabilizing Controllers for Nonlinear Control Systems

“…For convenience, a function V : D → R is said to be positive definite in D if V (x) > 0 for all x ∈ D \ {0} and V (0) = 0. It can be concluded from [30] that the system ( 7) is asymptotically stable with D being forward invariant and in the region of attraction if there exists a differentiable positive definite function…”

“…Next, simple reviews of the concept of CLFs [24] and CLBFs [30] will be introduced. Definition 2 ( [24]): A differentiable, proper, and positive definite function…”

“…By integrating CLFs and ZCBFs, a control synthesis methodology was developed using quadratic programs (QPs) to guarantee the satisfaction of state constraints. In [30], a new CLBF approach was proposed to solve the state-constrained stabilization problem. The construction of CLBFs and implementation of controllers are easier than those proposed in [21], [26]- [29].…”

“…The construction of CLBFs and implementation of controllers are easier than those proposed in [21], [26]- [29]. All controllers proposed in [8]- [30] are continuous controllers.…”

“…In this paper, we consider the design of event-triggered state-constrained stabilizing controllers for general nonlinear control-affine systems. The strong CLBF method, an extension of the new CLBF approach developed in [30], is used to first derive a state-constrained continuous stabilizing feedback law. Sufficient conditions are derived for the existence of strong CLBFs.…”