Hannah Michalska

Robust receding horizon control of constrained nonlinear systems

We present a method for the construction of a robust dual-mode, receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error. The controller is dual-mode. In a neighborhood of the origin, the control action is generated by a linear feedback controller designed for the linearized system. Outside this neighborhood, receding horizon control is employed. Existing receding horizon controllers for nonlinear, continuous time systems, which are guaranteed to stabilize the nonlinear system to which they are applied, require the exact solution, at every instant, of an optimal control problem with terminal equality constraints. These requirements are considerably relaxed in the dual-mode receding horizon controller presented in this paper. Stability is achieved by imposing a terminal inequality, rather than an equality, constraint. Only approximate minimization is required. A variable time horizon is permitted. Robustness is achieved by employing conservative state and stability constraint sets, thereby permitting a margin of error. The resultant dual-mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear, constrained systems. >

Receding horizon control of nonlinear systems

The receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems. The method is especially useful for the control of slow nonlinear systems, such as chemical batch processes, where it is possible to solve, sequentially, open-loop fixed-horizon, optimal control problems online. The method has been shown to yield a stable closed-loop system when applied to time-invariant or time-varying linear systems. It is shown that the method also yields a stable closed-loop system when applied to nonlinear systems. >

Moving horizon observers and observer-based control

In this paper two topics are explored. A new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed. The moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing, or approximately minimizing, a cost function over the preceding interval (horizon) [t-T,t]; as t advances, so does the horizon. Convergence of the estimator is established under the assumption that the corresponding global optimization problem can be (approximately) solved and a uniform reconstructability condition is satisfied; the latter condition is automatically satisfied for linear observable systems. The utility of the estimator for receding horizon control is explored. In particular, stability of a composite moving horizon system, comprising a moving horizon regulator and a moving horizon observer, is established. >

Receding horizon control of nonlinear systems without differentiability of the optimal value function

Abstract In this paper, we show that receding horizon control, when applied to a class of nonlinear systems, has stabilizing properties. Our assumptions are necessarily fairly strong because they guarantee implicity that a smooth stabilizing feedback can be constructed. This is an extension of our previous results which require the finite horizon value function to be continuously differentiable and therefore applies to a more restricted class of system. Continuous differentiability of the value function is replaced by local Lipschitz continuity; Dini derivatives and a generalization of the Invariance Principle are employed to establish stability.

Controllability and Posture Control of a Wheeled Pendulum Moving on an Inclined Plane

The paper considers a specific class of wheeled mobile robots, namely, mobile wheeled pendulums (MWPs). Robots pertaining to this class are composed of two wheels rotating about a central body. The main feature of MWP pertains to the central body, which can rotate about the wheel axis. As such motion is undesirable, the problem of the stabilization of the central body in an MWP is crucial. The novelty of the work reported here resides in the construction of: 1) the system controllability Lie algebra for the purpose of a rigorous controllability analysis and the computation of the largest feedback-linearizable subsystem; 2) a controller by input-output linearization of the system for achieving the desired steering rate of the robot while stabilizing the central body; 3) a controller based on the internal properties of the system to achieve the desired heading velocity of the robot; and 4) a controller based on the sliding-mode approach for controlling both the position and the orientation of the robot. The entire control structure that permits full control of the robot posture comprises three imbricated loops. Simulations showing good performance of the controlled system are provided. Preliminary tests performed on an experimental platform confirm the validity of the controller.

MOVING HORIZON OBSERVERS

Abstract A new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed. The observer produces an estimate of the state of the nonlinear system at time t, by minimizing, or approximately minimizing, a cost function over the interval (horizon) [t − T, t]; as t advances, so does the horizon. Two forms of the estimator are described. In the first, the cost is a function of the unknown state. In the second, an observer with control injection is employed, the injection v being obtained by the (approximate) solution of an optimal control problem. 1 he second approach is, in some sense, a dual form of receding horizon control which is an optimization-based method for designing globally stabilising feedback for nonlinear systems. Global convergence of the estimators is established.

Robust output feedback stabilization of uncertain time-varying state-delayed systems with saturating actuators

The robust output feedback stabilization problem for state-delayed systems with time-varying delays and saturating actuators is addressed here. The systems considered are continuous-time, with parametric uncertainties entering all the matrices in the system representation. A saturating control law is designed and a region of initial conditions is specified within which local asymptotic stability of the closed-loop system is ensured. The least conservative approach that employs the Lyapunov–Krasovskii functional is adopted to ensure stabilization. The designed controller is dependent on the time-delay and its rate of change. The controller is constructed in terms of the solution to a set of matrix inequalities.

Decision-Directed Adaptive Estimation and Guidance for an Interception Endgame

A new integrated estimation and guidance design approach is presented as a computationally effective procedure for interception of maneuvering targets. This is an adaptive approach that uses the following elements: banks of state estimators, and guidance laws, a maneuver detector for the onset of the target’s maneuver, and a hierarchical decision law for online selection of the estimator/guidance law pair to be employed. Simulation results confirm that the adaptive approach leads to a reduction in the miss distance as compared with cases in which only a single estimator/guidance law combination is available. LTHOUGH the study presented in this paper was motivated by a future ballistic missile defense (BMD) scenario, it addresses a more general problem, namely, the interception of a randomly maneuvering target by a guided missile in an environment of noise-corrupted measurements. The missile guidance endgame is an imperfect information terminal control problem with a very short horizon and it requires a design approach different from the one used in other control systems. In the classical approach, a linearized model of the dynamic process about a nominal set point is first derived. For this linearized model, the estimator and the control law are designed independently. The separate design is based on assuming the validity of the certainty equivalence principle (CEP) and the associated separation theorem (ST). 1

Vertical motion control of a hopping robot

We present a new approach for vertical motion feedback control of a hopping robot. The task of the feedback control is to stabilize the robotic system to a desired limit cycle under existing constraints on the controls. Unlike most previous methods, the approach presented here does not rely on the construction of the Poincare map, which simplifies the subsequent analysis, but can be difficult or impossible to obtain analytically. The method can also be applied to more complicated, possibly nonlinear models of legged robots, as well as other variable structure systems.

Novel Adaptive Generalized Likelihood Ratio Detector with Application to Maneuvering Target Tracking

A novel adaptive jump-detection algorithm is introduced for scenarios involving abrupt changes in the inputs to linear systems, such as those that might occur in tracking maneuvering targets. Improving upon the standard generalized likelihood ratio (GLR) detector, presented over two decades ago, the new algorithm is characterized by increased robustness with respect to uncertainties in the system input, which frequently arise in the context of target tracking applications. The performance of the new algorithm is demonstrated in an endgame scenario involving an interceptor missile and a maneuerable tactical ballistic missile. An extensive Monte Carlo simulation study is used to demonstrate the superiority of the method over the conventional GLR method in terms of its much smaller observed false alarm probability, which actually agrees with the theoretical value. The new algorithm also facilitates a correct isolation of the abrupt change, is consistent in the usual statistical sense, and generally proves more reliable.