Inverse optimal adaptive output feedback control of a class of Euler–Lagrange systems: A nonlinear filter based approach

In this paper, we present an inverse optimal tracking controller for a class of Euler–-Lagrange systems having uncertainties in their dynamical terms under the restriction that only the output state ( i.e. position for robotic systems) is available for measurement. Specifically, a nonlinear filter is used to generate a velocity substitute, then a controller formulation ensuring a globally asymptotically stable closed-loop system while minimizing a performance index despite the presence of parametric uncertainty, is proposed. The stability proof is established using a Lyapunov analysis of the system with proposed optimal output feedback controller. Inverse optimality is derived via designing a meaningful cost function utilizing the control Lyapunov function. Numerical simulations are presented to illustrate the viability and performance of the derived controller.

A critical evaluation of the index of patch quality

The inverse optimality approach can allow us to learn about an animal's environment by assuming their behaviour is optimal. This approach has been applied to animals diving underwater for food to produce the index of patch quality (IPQ), which aims to provide a proxy for prey abundance or quality in a foraging patch based on the animal's diving behaviour. The IPQ has been used in several empirical studies but has never been evaluated theoretically. Here, we discuss the strengths and weaknesses of the IPQ approach from a theoretical angle and review the empirical evidence supporting its use. We highlight several potential issues, in particular with the gain function—the function describing the energetic gain of an animal during a dive—used to calculate the IPQ. We investigate an alternative gain function which is appropriate in some cases, provide a new model based on this function, and discuss differences between the IPQ model and ours. We also find that there is little supporting empirical evidence justifying the general use of the IPQ and suggest future empirical validation methods which could help strengthen the case for the IPQ. Our findings have implications for the field of diving ecology and habitat assessment.

Universal Feedback Controllers and Inverse Optimality for Nonlinear Stochastic Systems

In this paper, we develop a constructive finite time stabilizing feedback control law for stochastic dynamical systems driven by Wiener processes based on the existence of a stochastic control Lyapunov function. In addition, we present necessary and sufficient conditions for continuity of such controllers. Moreover, using stochastic control Lyapunov functions, we construct a universal inverse optimal feedback control law for nonlinear stochastic dynamical systems that possess guaranteed gain and sector margins. An illustrative numerical example involving the control of thermoacoustic instabilities in combustion processes is presented to demonstrate the efficacy of the proposed framework.