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ABSTRACT: In this paper, we consider the problem of adaptive model predictive control subject to exogenous disturbances. Using a novel set-based adaptive estimation, the problem of robust adaptive MPC is proposed and solved for a class of linearly parameterized uncertain nonlinear systems subject to state and input constraints. Two formulations of the adaptive MPC routine are proposed. A general minmax approach is considered. A Lipschitz-based formulation is also proposed. The closed-loop robust stability of both approaches is demonstrated. The Lipschitz-based approach avoids the need for a minmax optimization problem and is amenable to real-time computation. A simple chemical reactor simulation example is presented that demonstrates the effectiveness of the technique. Copyright © 2010 John Wiley & Sons, Ltd.
International Journal of Adaptive Control and Signal Processing 08/2010; 25(2):155 - 167. · 0.91 Impact Factor
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ABSTRACT: The work presented in this chapter transcends beyond characterizing the parameter convergence rate. A method is presented for computing the exact parameter value at a finite-time selected according to the observed excitation in the system. A smooth transition from a standard estimate to the FT estimate is proposed. In the presence of unknown bounded disturbances, the FT identifier converges to a neighbourhood of the true value whose size is dictated by the choice of the filter gain. Moreover, the procedure preserves the system's established closed-loop properties whenever the required PE condition is not satisfied. We also demonstrate how the finite-time identification procedure can be used to improve the overall performance (both transient and steady state) of adaptive control systems in a very appealing manner. The adaptive compensator guarantees exponential convergence of the estimation error provided a given PE condition is satisfied. The convergence rate of the parameter estimator is directly proportional to the adaptation gain and a measure of the system's excitation. The adaptive compensator is then combined with existing adaptive controllers to guarantee exponential stability of the closed-loop system. The application reported in Section 9 is just an example, the adaptive compensator can easily be incorporated into other adaptive control algorithms.
01/2009; , ISBN: 978-953-7619-43-5
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ABSTRACT: 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.
Automatica. 01/2007; 43:105-110.
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ABSTRACT: Although there is great motivation for adaptive approaches to nonlinear model prediction control, few results to date can
guarantee feasible adaptive stabilization in the presence of state or input constraints. By adapting a set-valued measure
of the parametric uncertainty within the framework of robust nonlinear-MPC, the results of this paper establish such constrained
adaptive stability. Furthermore, it is shown that the ability to account for future adaptation has multiple benefits, including
both the ability to guarantee an optimal notion of excitation in the system without requiring dither injection, as well as
the ability to incorporate substantially less conservative designs of the terminal penalty.
01/1970: pages 55-67;
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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.
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ABSTRACT: 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.
Systems & Control Letters.
