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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 togetherwith 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 functionbased 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 statefeedback 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.

Explicit model predictive control (MPC) enhances application of MPC to areas where the fast online computation of the control signal is crucial, such as in aircraft or vehicle control. Explicit MPC controllers consist of several affine feedback gains, each of them valid over a polyhedral region of the state space. In this paper the optimal control of the quarter car semi-active suspension is studied. After a detailed theoretical introduction to the modeling, clipped LQ control and explicit MPC, the article demonstrates that there may exist regions where constrained MPC/explicit MPC has no feasible solution. To overcome this problem the use of soft constraints and combined clipped LQ/MPC methods are suggested. The paper also shows that the clipped optimal LQ solution equals to the MPC with horizon N = 1 for the whole union of explicit MPC regions. We study the explicit MPC of the semi-active suspension with actual discrete time observer connected to the explicit MPC in order to increase its practical applicability. The controller requires only measurement of the suspension deflection. Performance of the derived controller is evaluated through simulations where shock tests and white noise velocity disturbances are applied to a real quarter car vertical model. Comparing MPC and the clipped LQ approach, no essential improvement was detected in the control behavior. Keywords Explicit model predictive control • soft constraints • combined clipped LQ control/MPC • deterministic actual observer • passivity and saturation constraints • semi-active suspension • magneto-rheological (MR) damper.

In this article we propose a hierarchical control structure for multi-agent systems. The main objective is to perform formation change manoeuvres, with guaranteed safe distance between each two vehicles throughout the whole mission.The key components that ensure safety are a robust control algorithm that is capable of stabilising the group of vehicles in a desired formation and a higher level path generation method that provides all the vehicles with safe paths, based on graph theoretic considerations. The method can efficiently handle a large group of any type of vehicles. As an illustration, the results are applied to a group of quadrotor UAVs.