Filtering adaptive output feedback control for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics

Abstract

This article synthesizes a filtering adaptive output feedback controller for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The unmodeled dynamics are bounded-input bounded-output stable. By adopting an estimation/cancellation strategy, a piecewise constant adaptive law drives the estimation error to zero at every time instant, which yields the adaptive parameters; a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, while a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. A feedforward control law is designed to track a given command. Since the virtual reference system defines the best performance that can be achieved by the closed-loop system, the uniform performance bounds are derived for the states and control signals via comparison. Both numerical and practical examples are provided to illustrate the effectiveness of the proposed filtering adaptive output feedback control architecture, comparisons with the model reference adaptive control demonstrates the superiority of the proposed control method. K E Y W O R D S filtering adaptive control, mismatched uncertainties, nonlinear, output feedback, unmodeled dynamics How to cite this article: Ma T. Filtering adaptive output feedback control for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics.

Mixed H2/H∞ model reference control of linear parameter‐varying discrete‐time systems with real‐time application to aeropendulum system

“…Solve the LMIs (40)-(43) for 𝛾 2 , 𝛾 ∞ , P i , R i , G 1 and L si , (i = 0, 1, … , g). 4. Compute the following matrices of the input (32): K s (𝜙) using K s (𝜙) = L s (𝜙)G 1 −1 , Q s using (51) and F s (𝜙) using (52).…”

“…The topic of MRC, also known as model following control, has been investigated by many researchers for different types of systems. [1][2][3][4][5] The purpose of MRC is to force the system outputs to track the desired outputs of the reference model in the presence of different types of disturbances, noises, uncertainties, delays, faults, etc. For various types of systems, some of the studies related to the design of MRC systems are summarized in the following paragraphs.…”

“…An $$$ {H}_{\infty } $$$ decentralized observer‐based output‐feedback MRC method 12 is applied to LTI systems with bounded interconnected nonlinearity. The design of a filtering adaptive neural network controller 4,13 is applied to Lipschitz nonlinear systems to guarantee the closed‐loop system stability, robustness and tracking performance of the reference model outputs.…”

Robust Adaptive Fuzzy Fractional Control for Nonlinear Chaotic Systems with Uncertainties

“…On the other hand, fractional calculus, as an incipient field in mathematics, has been extensively used in many branches of physics and engineering sciences, such as control systems [26][27][28][29][30], dynamical systems [31], viscoelastic materials [32][33][34], signal and image processing [35], diffusion wave [36], biomedical applications [37], stochastic and chaotic systems [38], and heat systems [39]. However, most studies published in the last three decades have concentrated on the fractional PID controller [40][41][42].…”

Disturbance observer‐based two‐Layer control strategy design to deal with both matched and mismatched uncertainties

“…A comprehensive control scheme should consider both the robustness and the quality response of the considered systems (e.g., control effort minimization, settling time modification, and so forth). In this regard, several control approaches have been presented for making nonlinear systems robust against matched uncertainties 1‐7 and mismatched uncertainties, 8‐13 which are not in the range space of the input matrix. Due to their unique features, designing a controller that be able to optimally and robustly manage nonlinear systems subjected to mismatched uncertainties has been the desire of researchers.…”