Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has remained a non-trivial open problem. The control development in this paper guarantees ultimately bounded tracking of a desired trajectory, while also ensuring that the controller converges to an approximate optimal policy.

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A continuous saturated controller using smooth saturation functions is established for Macpherson active suspension system which includes nonlinear uncertainties, unknown road excitations and bounded disturbances. The developed controller exploits the properties of the hyperbolic functions to guarantee saturation limits are not exceeded, while stability analysis procedures of the robust integral of the sign of the error (RISE) control technique utilize the advantages of high gain control strategies in compensating for unknown uncertainties. The saturated controller guarantees asymptotic regulation of the sprung mass acceleration to improve the ride comfort despite model uncertainties and additive disturbances in the dynamics. Simulation results demonstrate the improvement in the ride comfort while tire deflection and the suspension deflection are within admissible range in comparison with three other suspensions.

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Abstract-Efforts in this paper seek to combine graph theory with adaptive dynamic programming (ADP) as a reinforcement learning (RL) framework to determine forward-in-time, realtime, approximate optimal controllers for distributed multi-agent systems with uncertain nonlinear dynamics. A decentralized continuous time-varying control strategy is proposed, using only local communication feedback from two-hop neighbors on a communication topology that has a spanning tree. An actorcritic-identifier architecture is proposed that employs a nonlinear state derivative estimator to estimate the unknown dynamics online and uses the estimate thus obtained for value function approximation. Simulation results demonstrate the applicability of the proposed technique to cooperatively control a group of five agents.

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