Is Input-to-state Stable Research Articles

Towards semi-autonomous operation of under-actuated underwater vehicles: sensor fusion, on-line identification and visual servo control

In this paper we propose a framework for semi-autonomous operation of an under-actuated underwater vehicle. The contributions of this paper are twofold: The first contribution is a visual servoing control scheme that is designed to provide a human operator the capability to steer the vehicle without loosing the target from the vision system's field of view. It is shown that the under-actuated degree of freedom is input-to-state stable (ISS) and a shaping of the user input with stability guarantees is implemented. The resulting control scheme has formally guaranteed stability and convergence properties. The second contribution is an asynchronous Modified Dual Unscented Kalman Filter (MDUKF) for the on-line state and parameter estimation of the vehicle by fusing data from a Laser Vision System (LVS) and an Inertial Measurement Unit (IMU). The MDUKF has been developed in order to experimentally verify the performance of the proposed visual servoing control scheme. Experimental results of the visual servoing control scheme integrated with the asynchronous MDUKF indicate the feasibility and applicability of the proposed control scheme. Experiments have been carried out on a small under-actuated Remotely Operated Vehicle (ROV) in a test tank.

ISS of interconnected impulsive systems with and without time-delays

We consider networks of impulsive systems with and without time-delays and investigate under which conditions the whole network is input-to-state stable (ISS). We provide conditions on the size of the time intervals between impulses and on the interconnection structure that guarantee ISS of the overall system, where Lyapunov and Lyapunov-Razumikhin functions for the subsystems are used. The condition on the interconnection allows to construct a Lyapunov (-Razumikhin) function and a corresponding gain for the whole system.

Input-to-state stability of robust receding horizon control with an expected value cost

This paper is concerned with the stability of a class of receding horizon control (RHC) laws for constrained linear discrete-time systems subject to bounded state disturbances and convex state and input constraints. The paper considers the class of finite horizon feedback control policies parameterized as affine functions of the system state, calculation of which can be shown to be tractable via a convex reparameterization. When minimizing the expected value of a finite horizon quadratic cost, we show that the value function is convex. When solving this optimal control problem at each time step and implementing the result in a receding horizon fashion, we provide sufficient conditions under which the closed-loop system is input-to-state stable (ISS).

A DECENTRALIZED MPC ALGORITHM FOR NONLINEAR SYSTEMS

In this paper a stabilizing decentralized MPC algorithm for discrete time nonlinear systems is presented. The method is developed by assuming that the overall system under control is composed by a number of subsystems, each one locally controlled with a closed-loop min-max MPC algorithm. The effect of interconnections is considered as a perturbation term. The main stability result is derived first by showing that each closed-loop sub-system is Input-to-State Stable (ISS) with respect to the effect of the interconnections and of the external disturbances and then, using a small gain theorem result, by proving that the over system is ISS with respect to external disturbances.

Optimization over state feedback policies for robust control with constraints

This paper is concerned with the optimal control of linear discrete-time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and all allowable disturbance sequences. The cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance-free state and input sequences. The value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic, or a tractable second-order cone program (SOCP) if the disturbance set is given by a 2-norm bound.

A note on input-to-state stability and averaging of systems with inputs

Two different definitions of an average for time-varying systems with inputs and a small parameter that were recently introduced in the literature are considered: and averages. It is shown that if the strong average is input-to-state stable (ISS), then the solutions of the actual system satisfy an integral bound in a semiglobal practical sense. The integral bound that we prove can be viewed as a generalization of the notion of finite-gain L/sub 2/ stability, that was recently introduced in the literature. A similar result is proved for weak averages but the class of inputs for which the integral bound holds is smaller (Lipschitz inputs) than in the case of strong averages (measurable inputs).

Robust input to state stabilization for minimum-phase nonlinear systems

The paper considers minimum-phase nonlinear systems that are subject to bounded parametric uncertainties. The parametric uncertainties are not required to enter linearly in the state equations. The problem addressed concerns the design of a nonlinear state feedback controller such that the closed-loop system is input to state stable (ISS) for any input belonging to Linfinity [0,infinity) . Based on the normal form of a nonlinear minimum-phase system, a robust ISS controller is designed by applying the so-called 'backstepping'technique. Furthermore, the L2-gain from the input to the output of the closed-loop system is guaranteed to be less than or equal to a prespecified level for all admissible uncertainties.