Integral reinforcement learning with explorations for continuous-time nonlinear systems

This paper focuses on the integral reinforcement learning (I-RL) for input-affine continuous-time (CT) nonlinear systems where a known time-varying signal called an exploration is injected through the control input. First, we propose a modified I-RL method which effectively eliminates the effects of the explorations on the algorithm. Next, based on the result, an actor-critic I-RL technique is presented for the same nonlinear systems with completely unknown dynamics. Finally, the least-squares implementation method with the exact parameterizations is presented for each proposed one which can be solved under the given persistently exciting (PE) conditions. A simulation example is given to verify the effectiveness of the proposed methods.