Control of MIMO nonlinear systems: A data-driven model inversion approach

In this paper, we propose a numerical technique for reference tracking control of discrete-time MIMO nonlinear systems. The technique is based on the derivation of an auxiliary predictor model and on the online computation of an approximate model inversion control sequence. If the predictor model is assumed to be polynomial, then the control input is computed at each time interval by solving a polynomial optimization problem by means of a cyclic coordinate minimization technique. This technique is numerically efficient and guarantees convergence to a so-called coordinate-wise minimum point. We provide a formal proof for boundedness of the tracking error and closed-loop stability of approximate model inversion control. A numerical example involving therapy control for a diabetic patient illustrates the practical potential of the proposed method.

This paper proposes a new approach of adaptive sliding mode controller designs for multiple-input multiple-output nonlinear systems with uncertainties of unknown bounds and limited available inputs. The goal is to obtain robust, smooth, and fast transient performance for real sliding mode control so that the phenomena of the slow response and the gain overestimation in most adaptive sliding mode controller designs can be greatly improved. We introduce an Integral/Exponential adaptation law with boundary-layer targeting the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously speeding up the system response to the uncertainties. The gain is further reduced when the system state is in the boundary layer. The simulation and experimental results demonstrate the proposed design. Copyright © 2016 John Wiley & Sons, Ltd.

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In this paper, a stable adaptive neural sliding mode controller is developed for a class of multivariable uncertain nonlinear systems. For these systems not all state variables are available for measurements. By designing a state observer, adaptive neural systems, which are used to model unknown functions, can be constructed using the state estimations. Based on Lyapunov stability theorem, the proposed adaptive neural control system can guarantee the stability of the whole closed loop system and obtain good tracking performances. Adaptive laws are proposed to adjust the free parameters of the neural models. Simulation results illustrate the design procedure and demonstrate the tracking performances of the proposed controller.

SummaryA new robust iterative learning control scheme is presented for state tracking control of nonlinear MIMO systems. The main characteristic of the proposed controller lies in its ability to deal with unstructured uncertainties that are norm‐bounded but not globally or locally Lipschitz continuous as usual. The classical resetting condition of iterative learning control is removed and replaced with more practical alignment condition. The class of systems to be considered is further extended to more general scenarios, in which input distribution uncertainties are included. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed control scheme. Copyright © 2015 John Wiley & Sons, Ltd.

This work proposes a method to construct a state-shared model for multiple-input multiple-output (MIMO) systems. A state-shared model is defined as a linear time invariant state-space structure that is driven by measurement signals-the plant outputs and the manipulated variables, but shared by different multiple input/output models. The genesis of the state-shared model is based on a particular reduced non-minimal realization. Any such realization necessarily fulfills the requirement that the output of the state-shared model is an asymptotically correct estimate of the output of the plant, if the process model is selected appropriately. The approach is demonstrated on a nonlinear MIMO system — a physiological model of calcium fluxes that controls muscle contraction and relaxation in human cardiac myocytes.

High gain adaptive output feedback control of MIMO nonlinear systems

We have studied the comment about our original paper and we agree that a minor mistake was made in Eq. 37 of our original paper (see ibid., vol. 11, no. 3, p. 354-60 (2003)).

Adaptive multi-tan-combined command-filtered control for MIMO nonlinear systems with novel error compensation signals

Finite-time-prescribed performance-based adaptive command filtering control for MIMO nonlinear systems with unknown hysteresis

SummaryThis paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme.

Motivated by the recent advance in adaptive output feedback control of affine nonlinear systems [8-10], an adaptive variable structure controller is proposed in this paper for solving the model reference adaptive control of nonlinear time-varying systems. Asymptotic output tracking performance can be achieved for relative degree one case. When the relative degree of the nonlinear system is greater than one, a systematic design procedure is given under a modified sector-type condition so that the closed-loop stability and the tracking performance are achieved similar to that in relative degree one case.

Operator based nonlinear vibration control design for a multiple input multiple output(MIMO) wing-plate system is considered. For considering the MIMO wing-plate system with the effect of the coupling from the piezoelectric actuator(PEA)'s moments, the bounded input bounded output(BIBO) stability of the system is considered based on operator theory. Simultaneously, for obtaining the desired vibration control performance, the operators are designed to compensate for the external force and coupling's effects. Finally, the effectiveness of the designed nonlinear control system is confirmed by the numerical simulation.

Higher order nonlinear systems with prevailing delay have been very challenging in significance with stability and process performance. This paper investigates the performance of a type-2 Mamdani intelligent controller implemented a delay dominant system which is modelled using black box approach identified to be a second order nonlinear model for a dual spherical tank liquid level system (DSTLLS) under LabVIEW environment. The adaptive approach of the intelligent Mamdani-based fuzzy controller proves itself to be very competent compared with the earlier experimented methods that already exist. The performance indices like integrated absolute error (IAE) and integrated squared error (ISE) are also calculated for different varying set point changes of DSTLLS. The response and error reduction efficiency of this method of adaptive type-2 intelligent fuzzy (ATIF) controller has been experimented for different flow configurations of this DSTLLS, like multiple input single output (MISO), multiple input multiple output (MIMO) and single input single output (SISO).

This work proposes a discrete-time non-linear neural observer based on a recurrent high order neural network in parallel model trained with an algorithm based on the extended Kalman filter for discrete-time multiple input multiple output non-linear systems with unknown dynamics and unknown time-delay. To prove the semi-globally uniformly ultimately boundedness of the proposed neural observer the stability analysis based on the Lyapunov approach is included. Applicability of the proposed observer is shown via simulation and experimental results.