This paper studies the problem of global state regulation with stability for time-delay nonlinear systems with unknown control directions. Using a dynamic gain-based approach for counteracting time-delay nonlinearity and the Nussbaum-gain function for dealing with unknown control directions, we develop a dynamic state feedback control strategy that solves the problem. A novel construction of Lyapunov-Krasovskii functionals is presented and plays a key role in handling nonlinearity with delayed states and unknown control directions simultaneously. The proposed dynamic state feedback compensators are shown to guarantee: i) global asymptotic convergence of the system state to the origin; and ii) global boundedness of the resulted closed-loop systems

SUMMARY: In this paper, we study the problem of adaptive position tracking for a multi-link robot driven by two opposing pneumatic muscle groups with additive disturbances. In contrast to widely used sliding mode control methods, the proposed controller is continuous and able to prevent chattering. All physical parameters of the robot and the pneumatic muscles, including pneumatic muscle coefficients, link lengths and moments of inertia are unknown and can be time-varying and the unknown additive disturbances can be discontinuous. Under these conditions, we prove that closed-loop trajectories of all of the joint positions can track anyC¹joint reference signal. The joint errors will be within a prescribed error bound in a finite time. The adaptive controller only uses the reference signal, not its derivative. The continuous adaptive gain is one-dimensional. Simulations including a two-link robot arm with friction and realistic muscle models are presented to demonstrate the robustness of the adaptive control under severe changes of the system parameters. In all simulations, the joint positions can trackC¹trajectories and all errors are within the prescribed error bound in the same time frame, even though the muscle parameters are vastly different.

Adaptive control of general nonlinear systems with nonlinear parameterization is studied in this paper. Under the assumptions that the system has stable free dynamics and satisfies controllability-like conditions characterized by the Lie brackets of affine vector fields, it is proved that there exist L_gV-type adaptive controllers that not only asymptotically regulate the state of the nonlinearly parameterized system but also guarantee global stability of the closed-loop system. The design of L_gV-type adaptive controllers is also included. Applications of the proposed adaptive control scheme are presented, including an interesting case of a DC-microgrid with PV and battery system.