Explicit MPC-Based RBF Neural Network Controller Design With Discrete-Time Actual Kalman Filter for Semiactive Suspension

Many applications require fast control action and efficient constraint handling, such as in aircraft or vehicle control, where instead of the slow online computation of the model predictive control (MPC) the explicit MPC can be an alternative solution. Explicit MPC controllers consist of several affine feedback gains, each of them valid over a polyhedral region of the state space. The exponential blow-up of the number of regions with increasing the prediction horizon increases the searching time among the regions extremely which together with the requirement of the full state measurement decreases its applicability for real systems. First, discrete-time actual Kalman filter is designed for the semiactive suspension and applied to explicit MPC controller that requires only measurement of the suspension deflection. Second, this paper presents a systematic way to design Gaussian radial basis function-based neural network (NN) approximation of the explicit MPC controller and shows that a well-tuned NN with some neurons can replace the explicit MPC controller. This nonlinear state-feedback controller can ensure the fast control action but price of the approximation is some deterioration of the performance value. The complete novel nonlinear control system with Kalman filter is analyzed in detail. The derived controllers are evaluated through simulations, where shock tests and white noise velocity disturbances are applied to a real quarter car vertical model.