Model Reference Adaptive Control for Multi-Input Multi-Output Nonlinear Systems Using Neural Networks

This paper presents a method of MRAC(model reference adaptive control) for multi-input multi-output(MIMO) nonlinear systems using NNs(neural networks). The control input is given by the sum of the output of a model reference adaptive controller and the output of the NN(neural network). The NN is used to compensate the nonlinearity of plant dynamics that is not taken into consideration in the usual MRAC. The role of the NN is to construct a linearized model by minimizing the output error caused by nonlinearities in the control systems. INTRODUCTION MRAC is an important class of adaptive control scheme [1],[2]. In the direct MRAC scheme, the regulator is updated online so that the plant output follows the output of a reference model. In the MRAC of linear plant, the reference model and the controller structure are chosen in such a way that a parameter set of the regulator exists to ensure perfect model following [3],[4]. However, for nonlinear plants with unknown structures, it may not be possible to ensure perfect model following [5]. This paper presents a structure of MRAC system for MIMO nonlinear systems using NNs. The control input is given by the sum of the output of a model reference adaptive controller and the output of the NN. The role of the NN is to compensate for constructing a linearized model so as to minimize an output error caused by nonlinearities in the control system. The role of model reference adaptive controller is to perform the model matching for the uncertain linearized system to a given linear reference model. One of the distinctive features of the proposed structure is to give an efficient method for calculating the derivative of the system output with respect to the input by using one identified parameter in the linearized model and the internal variables of the NN, which enables to perform the backpropagation algorithm very efficiently. Furthermore, in the proposed method, if the plant is linear, it is unique that neural network does not need to operate. Finally, the computer simulation is done and the effectiveness of this control system is confirmed. LINEAR MRAC In this section, we briefly describe a MIMO linear discretetime MRAC, where the controller is designed to realize a plant output Y (k) converges to reference model output Ym(k). Let us consider the MIMO linear discrete-time system described by A(z)Y (k) = diag(z−di)B(z)U(k) (1) where A(z) = diag[A1(z), · · · , Ap(z)], B(z) =   z−d11+d1B11(z) · · · z−d1p+d1B1p(z) .. . . . .. z−dp1+dpBp1(z) · · · z−dpp+dpBpp(z)   and diag(z−di) = diag[z−d1 , · · · , z−dp ]. Ai(z) and Bij(z)(i = 1, · · · , p; j = 1, · · · , p) are scalar polynomials, and dij (i = 1, · · · , p; j = 1, · · · , p) represent the known time delay. Furthermore, U(k) ∈ Rp×1 is the system input vector and Y (k) ∈ Rp×1 is the system output vector, and di = min1≤j≤pdij(i = 1, · · · , p). The matrices A(z) and B(z) are given by