ABSTRACT
In the previous chapter, we looked at Q-learning-based optimal control synthesis techniques suitable for uncertain linear discrete-time systems using state and output feedback when the communication network in the feedback loop is lossless as well as when it is lossy. In the first part of this chapter, based on the work in Sahoo, et al., 2016a, we shall consider multi-input-multi-output (MIMO) uncertain nonlinear continuous-time (CT) systems in affine form. In particular, we shall develop an approximation-based event-triggered controller suitable for MIMO nonlinear CT systems whose dynamics are represented in affine form. The controller utilizes a linearly parameterized neural network (NN) whose weights are tuned using data that are sampled based on aperiodic events. In this context, we shall revisit the NN approximation property with event-based sampling, develop an event-trigger condition by using the Lyapunov technique to reduce the network resource utilization and generate the required number of events for the NN approximation.
In the second part of this chapter, based on the work in Sahoo, et al., 2017, we shall develop approximate optimal controllers for the uncertain nonlinear CT systems using adaptive dynamic programming (ADP) with event-sampled state and input vectors. In this case, we shall incorporate NNs to not only mitigate the need for an accurate model of the system dynamics but also learn the optimal value function, which becomes an approximate solution to the Hamilton-Jacobi-Bellman equation associated with the optimal control problem. For both the non-optimal and optimal controllers presented in this chapter, we shall also develop weight tuning rules to train the NNs online with aperiodic feedback data, design event-triggering conditions, derive sufficient conditions for closed-loop stability, and develop arguments to compute a positive lower bound on the minimum inter-sample time.
