Veronica Adetola

Adaptive model predictive control for constrained nonlinear systems

In this paper, a method is proposed for the adaptive model predictive control of constrained nonlinear system. Rather than relying on the inherent robustness properties of standard NMPC, the developed technique explicitly account for the transient effect of parametric estimation error by combining a parameter adjustment mechanism with robust MPC algorithms. The parameter estimation routine employed guarantees non-increase of the estimation error vector. This means that the controller employs a process model which approaches that of the true system over time. These estimates are used to update the parameter uncertainty set at every time step, resulting in a gradual reduction in the conservative and/or computational effects of the incorporated robust features.

Finite-Time Parameter Estimation in Adaptive Control of Nonlinear Systems

In most adaptive control algorithms, parameter estimate errors are not guaranteed to converge to zero. This lack of convergence adversely affects the global performance of the algorithms. The effect is more pronounced in control problems where the desired reference set-point or trajectory depends on the systems unknown parameters. In this paper, we present a parameter estimation routine that allows exact reconstruction of the unknown parameters in finite time provided a given excitation condition is satisfied. The algorithm is independent of the control and identifier structure employed. The true parameter value is obtained without requiring the measurement or computation of the velocity state vector. The technique provides a direct solution to the problem of removing auxiliary perturbation signals when parameter convergence is achieved. The effectiveness of the proposed method is illustrated with simulation examples.

Brief paper: Parameter convergence in adaptive extremum-seeking control

This paper addresses the problem of parameter convergence in adaptive extremum-seeking control design. An alternate version of the popular persistence of excitation condition is proposed for a class of nonlinear systems with parametric uncertainties. The condition is translated to an asymptotic sufficient richness condition on the reference set-point. Since the desired optimal set-point is not known a priori in this type of problem, the proposed method includes a technique for generating perturbation signal that satisfies this condition in closed-loop. This demonstrates its superiority in terms of parameter convergence. The method guarantees parameter convergence with minimal but sufficient level of perturbation. The effectiveness of the proposed method is illustrated with a simulation example.

Parameter estimation of a building system model and impact of estimation error on closed-loop performance

Predictive-control methods have been recently employed for demand-response control of building and district-level HVAC systems. Such approaches rely on models and parameter estimates to meet comfort constraints and to achieve the theoretical system-efficiency gains. In this paper we present a methodology that establishes achievable targets for control-model parameter estimation errors based on closed-loop performance sensitivity. The control algorithm is designed as a Model Predictive Controller (MPC) that uses perturbed building-model parameters. We perform simulations to estimate the dependency of energy cost and constraint infringement time on the magnitude of these perturbations. The simulation results are used to define targets for the parameter estimation errors, which in turn are applied to specify the character of excitation and model structure used for identification. We design a parameter estimator and perform Monte-Carlo simulations for a model that includes sensor noise and load uncertainty. The distribution of the estimation errors are used to demonstrate that the established targets are met.

PARAMETER CONVERGENCE IN ADAPTIVE EXTREMUM SEEKING CONTROL

This paper addresses the problem of parameter convergence in adaptive extremum seeking control design. An alternate version of the popular persistence of excitation condition is proposed for a class of nonlinear systems with parametric uncertainties. The condition is translated to an asymptotic sufficient richness condition on the reference set-point. Since the desired optimal set-point is not known a priori in this type of problem, the proposed method includes a technique for generating perturbation signal that satisfies this condition in closed loop. This demonstrates its superiority in terms of parameter convergence. The method guarantees parameter convergence with minimal but sufficient level of perturbation. The effectiveness of the proposed method is illustrated with a simulation example.

Finite-time Parameter Estimation in Adaptive Control of Nonlinear Systems

This note presents a parameter estimation routine that allows exact reconstruction of the unknown parameters in finite time provided a given excitation condition is satisfied. The robustness of the routine to an unknown bounded disturbance or modeling error is also shown. The result is independent of the control and identifier structures employed. The true parameter value is obtained without requiring the measurement or computation of the velocity state vector. Moreover, the technique provides a direct solution to the problem of removing auxiliary perturbation signals when parameter convergence is achieved.

Adaptive receding horizon control of nonlinear systems

Abstract In this paper, a method is proposed for the adaptive receding horizon control of nonlinear systems. The method is based on known receding horizon control methods that employ control Lyapunov functions. The method proposed uses input to state stabilizing control Lyapunov functions to ensure stability and achieve a certain level of performance. A simulation example is provided to illustrate the applicability of the proposed Adaptive RHC + CLF method.

Excitation Signal Design for Parameter Convergence in Adaptive Control of Linearizable Systems

In most adaptive control approaches, parameter convergence to their true values can only be ensured if the closed-loop trajectories provide sufficient excitation for the parameter estimation method. In this paper, the design of excitation signal for the adaptive control of linearizable systems is investigated. Based on a sufficient richness condition, two approaches for generating perturbation signals to achieve a desired level of excitation are presented. Moreover, since constant persistently exciting input may deteriorates control performance, we provide a formal design technique for adjusting the excitation magnitude on-line to meet the conflicting objectives of control and identification. The algorithm attenuates the PE signal as parameter convergence is achieved and re-activates it only when required. A simulation example is used to illustrate the developed procedure and ascertain our theoretical results

Performance improvement in adaptive control of nonlinear systems

This paper demonstrates how the finite-time identification procedure [1] can be used to improve the overall performance of adaptive control systems. First, we develop an adaptive compensator which guarantees exponential convergence of the estimation error provided the integral of a filtered regressor matrix is positive definite. The approach does not involve online checking of matrix invertibility and computation of matrix inverse nor switching between parameter estimation methods. The convergence rate of the parameter estimator is directly proportional to the adaptation gain and a measure of the systems excitation. The adaptive compensator is then combined with existing adaptive controllers to guarantee exponential stability of the closed-loop system. The effectiveness of the proposed method is illustrated with simulation examples.

Adaptive Model Predictive Control for Constrained Nonlinear Systems

Abstract A true adaptive nonlinear model predictive control (MPC) algorithm must address the issue of robustness to model uncertainty while the estimator is evolving. Unfortunately, this may not be achieved without introducing extra degree of conservativeness and/or computational complexity in the controller calculations. To attenuate this problem, we employ a finite time identifier and propose an adaptive predictive control structure that reduces to a nominal MPC problem when exact parameter estimates are obtained. The adaptive MPC is formulated in such a way that useful excitation is automatically injected into the closed loop system to decrease the identification period.