Zhong Ping Jiang

Small-gain theorem for ISS systems and applications

We introduce a concept of input-to-output practical stability (IOpS) which is a natural generalization of input-to-state stability proposed by Sontag. It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is again an IOpS system if an appropriate composition of the gain functions is smaller than the identity function. The second one shows an example of gain function assignment by feedback. As an illustration of the interest of these results, we address the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.

Tracking control of mobile robots: a case study in backstepping

A tracking control methodology via time-varying state feedback based on the backstepping technique is proposed for both a kinematic and simplified dynamic model of a two-degrees-of-freedom mobile robot. We first address the local tracking problem where initial tracking errors are sufficiently small. Then, under additional conditions on the desired velocities, we treat the global tracking problem where initial tracking errors are arbitrary. Simulation results are provided to validate and analyse our theoretical results.

Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties

In this paper, a modified adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainty: (i)unknown parameters; (ii)uncertain nonlinearities and (iii)unmodeled dynamics. Nonlinear damping terms are used to counteract the uncertain nonlinear functions and a dynamic signal is introduced to dominate the dynamic disturbance. The derived adaptive controller guarantees the global boundedness property for all signals and states and at the same time, steers the output to a small neighborhood of the origin. Incidentally an adaptive output-feedback control problem is solved.

A recursive technique for tracking control of nonholonomic systems in chained form

The authors address the tracking problem for a class of nonholonomic chained form control systems. A recursive technique is proposed which appears to be an extension of the currently popular integrator backstepping idea to the tracking of nonholonomic control systems. Conditions are given under which the problems of semiglobal tracking and global path-following are solved for a nonholonomic system in chained form and its dynamic extension. Results on local exponential tracking are also obtained. Two physical examples of an articulated vehicle and a knife edge are provided to demonstrate the effectiveness of our algorithm through simulations.

A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems

The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear small-gain theorem for interconnected input/state-stable (ISS) systems. An ISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.

Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems

In this paper, the problem of decentralized adaptive output-feedback stabilization is investigated for large-scale stochastic nonlinear systems with three types of uncertainties, including parametric uncertainties, nonlinear uncertain interactions and stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystems are stochastic input-to-state stable, an adaptive output-feedback controller is constructively designed by the backstepping method. It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability. In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin. The contributions of the work are characterized by the following novel features: (1) even for centralized single-input single-output systems, this paper presents a first result in stochastic, nonlinear, adaptive, output-feedback asymptotic stabilization; (2) the methodology previously developed for deterministic large-scale systems is generalized to stochastic ones. At the same time, novel small-gain conditions for small signals are identified in the setting of stochastic systems design; (3) both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states; (4) parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields, which may appear nonlinearly; (5) the concept of stochastic input-to-state stability and the method of changing supply functions are adapted, for the first time, to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control.

A Distributed Control Approach to A Robust Output Regulation Problem for Multi-Agent Linear Systems

In this note, the robust output regulation problem of a multi-agent system is considered. An internal model based distributed control scheme is adopted to achieve the objectives of asymptotic tracking and disturbance rejection in an uncertain multi-agent system where both the reference inputs and disturbances are generated by an exosystem.

A small-gain control method for nonlinear cascaded systems with dynamic uncertainties

Some robust control problems for a class of nonlinear cascaded systems in the presence of state and input driven unmeasured dynamics are analyzed. A stepwise constructive control methodology is proposed on the basis of the nonlinear small-gain theorem. The flexibility of the approach in tackling dynamic uncertainties is illustrated by demonstrating that several results for special classes of cascaded systems, considered previously in the literature, may be viewed as special instances of the present results.

Robust exponential regulation of nonholonomic systems with uncertainties

This paper deals with nonholonomic control systems in chained form with strongly nonlinear disturbances and drift terms. The objective is to design a robust nonlinear state and output feedback law which simultaneously solves the global exponential regulation problem for all plants in the class. A switching control strategy is employed to get around the smooth stabilization burden associated with nonholonomic systems. The systematic strategy involves the introduction of a state-scaling technique and the application of the so-called integrator backstepping procedure. For the output feedback case, an interlaced observer/controller scheme is introduced for nonholonomic systems design. While earlier controllers fail to maintain robustness in the face of small disturbances, the simulation results based on some practical examples demonstrate the efficiency and robust features of the method proposed in this paper.

A Lyapunov–Krasovskii methodology for ISS and iISS of time-delay systems

Abstract This paper presents a Lyapunov–Krasovskii methodology for studying the input-to-state stability and the integral input-to-state stability of nonlinear time-delay systems. An integral input-state estimate which takes into account non-zero initial conditions is also proposed.