Global Output‐Feedback Stabilization for Stochastic Nonlinear Systems with Function Control Coefficients

This paper investigates the global output‐feedback stabilization for a class of stochastic nonlinear systems with function control coefficients. Notably, the systems in question possess control coefficients that are functions of output, rather than constants; hence, they are different from the existing literature on stochastic stabilization. To solve the control problem, an appropriate reduced‐order observer is introduced to reconstruct the unmeasured system states before a smooth output‐feedback controller is designed using the backstepping method, which guarantees that the closed‐loop system is globally asymptotically stable in probability. This paper combines the related results in the deterministic and stochastic setting and gives the first treatment on the global output‐feedback stabilization for the stochastic nonlinear systems with function control coefficients. A simulation example is given also to illustrate the effectiveness of the proposed approach.     

Trajectory Control of Snake‐Like Robots in Natural Oscillation

A class of body movement patterns called natural oscillation has been revealed to mimic the gaits observed in many animals. In this paper, we introduce an additional higher level control loop that is capable of manipulating a robot's motion orientation. With such a new orientation turning functionality, a snake‐like robot is able to achieve trajectory tracking while maintaining its body in a natural oscillation gait. The effectiveness of the control design is illustrated by some case studies with various trajectories.     

Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

This paper proposes a synthesis method of gain‐scheduled control systems that switch linear time‐invariant controllers according to hysteresis of the scheduling parameter. Stability and L₂‐gain analysis and synthesis methods for switched systems are applied to the switched gain‐scheduled control synthesis using reset of the controller state, where also the reset law is computed via linear matrix inequalities (LMIs). In addition to optimization of an upper bound of L₂‐gain, we reduce jumps of control input via an auxiliary optimization. Numerical examples are presented to illustrate the switched gain‐scheduled controller.     

Time Averaging Algorithms with Stopping Rules for Multi‐Agent Consensus with Noisy Measurements

A time averaging technique is introduced to consensus algorithms in networked multi‐agent systems under a noisy environment. Each agent communicates with its neighboring agents via a constant gain, while the time averaging states of the agents are considered as the values for agreement. The variation of the time averaging states then is evaluated at a specific number of iterations, where the number is given explicitly in terms of parameters related to the consensus accuracy and its probabilistic guarantee. This result establishes a rigorous stopping rule for the multi‐agent consensus with noisy measurements. Several results on this type of stopping rules are provided for undirected, directed, and time‐varying communication graphs. These theoretical results are illustrated through numerical examples.     

Robust non‐fragile H ∞ ∕ L2 − L ∞ control of uncertain linear system with time‐delay and application to vehicle active suspension

This paper presents an approach to design robust non‐fragile H _∞ ∕ L₂ ? L _∞ static output feedback controller, considering actuator time‐delay and the controller gain variations, and it is applied to design vehicle active suspension. According to suspension design requirements, the H _∞ and L₂ ? L _∞ norms are used, respectively, to reflect ride comfort and time‐domain hard constraints. By employing a delay‐dependent Lyapunov function, existence conditions of delay‐dependent robust non‐fragile static output feedback H _∞ controller and L₂ ? L _∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities. Then, a new procedure based on LMI optimization and a hybrid algorithm of the particle swarm optimization and differential evolution is used to solve an optimization problem with bilinear matrix inequality constraints. Simulation results show that the designed active suspension system still can guarantee their own performance in spite of the existence of the model uncertainties, the actuator time‐delay and the controller gain variations. Copyright © 2014 John Wiley & Sons, Ltd.     

Input‐output triggered control using ‐stability over finite horizons

This paper investigates stability of nonlinear control systems under intermittent information. Following recent results in the literature, we replace the traditional periodic paradigm, where the up‐to‐date information is transmitted and control laws are executed in a periodic fashion, with the event‐triggered paradigm. Building on the small gain theorem, we develop input–output triggered control algorithms yielding stable closed‐loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise in the environment, the developed algorithm yields stable, asymptotically stable, and ‐stable (with bias) closed‐loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on ‐stability are presented. The prediction of a triggering event is achieved by employing ‐gains over a finite horizon. By resorting to convex programming, a method to compute ‐gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking problem for unicycles. Copyright © 2014 John Wiley & Sons, Ltd.     

An analysis of the exponential stability of linear stochastic neutral delay systems

This paper is concerned with the analysis of the mean square exponential stability and the almost sure exponential stability of linear stochastic neutral delay systems. A general stability result on the mean square and almost sure exponential stability of such systems is established. Based on this stability result, the delay partitioning technique is adopted to obtain a delay‐dependent stability condition in terms of linear matrix inequalities (LMIs). In obtaining these LMIs, some basic rules of the Ito calculus are also utilized to introduce slack matrices so as to further reduce conservatism. Some numerical examples borrowed from the literature are used to show that, as the number of the partitioning intervals increases, the allowable delay determined by the proposed LMI condition approaches h_max, the maximal allowable delay for the stability of the considered system, indicating the effectiveness of the proposed stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Sufficient conditions for stability and stabilization of networked control systems with uncertainties and nonlinearities

In this paper, we consider the problem of robust stability and stabilization for networked control systems (NCS) with uncertain/nonlinear dynamics AUTHOR: Please check that authors and their affiliations are correct. in which the network‐induced delays are time‐varying and bounded. Based on some recent achievements, a relatively simple Lyapunov–Krasovskii functional is proposed to derive sufficient conditions both for analysis and synthesis of NCS in the form of LMIs depending on the delay bounds. The effectiveness of the proposed method is illustrated by several benchmark examples available in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Distributed formation control with relaxed motion requirements

Heterogeneous formation shape control with interagent bearing and distance constraints involves the design of a distributed control law that ensures the formation moves such that these interagent constraints are achieved and maintained. This paper looks at the design of a distributed control scheme to solve different formation shape control problems in an ambient two‐dimensional space with bearing, distance and mixed bearing and distance constraints. The proposed control law allows the agents in the formation to move in any direction on a half‐plane and guarantees that despite this freedom, the proposed shape control algorithm ensures convergence to a formation shape meeting the prescribed constraints. This work provides an interesting and novel contrast to much of the existing work in formation control where distance‐only constraints are typically maintained and where each agent's motion is typically restricted to follow a very particular path. A stability analysis is sketched, and a number of illustrative examples are also given. Copyright © 2014 John Wiley & Sons, Ltd.     

High‐precision formation control of nonlinear multi‐agent systems with switching topologies: A learning approach

Arbitrary high precision is considered one of the most desirable control objectives in the relative formation for many networked industrial applications, such as flying spacecrafts and mobile robots. The main purpose of this paper is to present design guidelines of applying the iterative schemes to develop distributed formation algorithms in order to achieve this control objective. If certain conditions are met, then the control input signals can be learned by the developed algorithms to accomplish the desired formations with arbitrary high precision. The systems under consideration are a class of multi‐agent systems under directed networks with switching topologies. The agents have discrete‐time affine nonlinear dynamics, but their state functions do not need to be identical. It is shown that the learning processes resulting from the relative output formation of multi‐agent systems can converge exponentially fast with the increase of the iteration number. In particular, this work induces a distributed algorithm that can simultaneously achieve the desired relative output formation between agents and regulate the movement of multi‐agent formations as desired along the time axis. The illustrative numerical simulations are finally performed to demonstrate the effectiveness and performance of the proposed distributed formation algorithms. Copyright © 2014 John Wiley & Sons, Ltd.