Keng Peng Tee

Barrier Lyapunov Functions for the control of output-constrained nonlinear systems

In this paper, we present control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint. To prevent constraint violation, we employ a Barrier Lyapunov Function, which grows to infinity when its arguments approach some limits. By ensuring boundedness of the Barrier Lyapunov Function in the closed loop, we ensure that those limits are not transgressed. Besides the nominal case where full knowledge of the plant is available, we also tackle scenarios wherein parametric uncertainties are present. Asymptotic tracking is achieved without violation of the constraint, and all closed loop signals remain bounded, under a mild condition on the initial output. Furthermore, we explore the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions. We also compare our control with one that is based on a Quadratic Lyapunov Function, and we show that our control requires less restrictive initial conditions. A numerical example is provided to illustrate the performance of the proposed control.

Adaptive Neural Control for Output Feedback Nonlinear Systems Using a Barrier Lyapunov Function

In this brief, adaptive neural control is presented for a class of output feedback nonlinear systems in the presence of unknown functions. The unknown functions are handled via on-line neural network (NN) control using only output measurements. A barrier Lyapunov function (BLF) is introduced to address two open and challenging problems in the neuro-control area: 1) for any initial compact set, how to determine a priori the compact superset, on which NN approximation is valid; and 2) how to ensure that the arguments of the unknown functions remain within the specified compact superset. By ensuring boundedness of the BLF, we actively constrain the argument of the unknown functions to remain within a compact superset such that the NN approximation conditions hold. The semiglobal boundedness of all closed-loop signals is ensured, and the tracking error converges to a neighborhood of zero. Simulation results demonstrate the effectiveness of the proposed approach.

Approximation-based control of nonlinear MIMO time-delay systems

Approximation-based control is presented for a class of multi-input multi-output (MIMO) nonlinear systems in block-triangular form with unknown state delays. Neural networks (NNs) are utilized to approximate and compensate for unknown functions in the system dynamics, including the unknown bounds of the functions of delayed states. The use of a separation technique removes the need for any assumption on the function of delayed states, and allows the handling of multiple delays in each function of delayed states. By combining the use of Lyapunov-Krasovskii functionals and adaptive NN backstepping, the proposed control guarantees that all closed-loop signals remain bounded, while the outputs converge to a neighborhood of the desired trajectories. Simulation results demonstrate the effectiveness of the proposed scheme.

Brief paper: Control of nonlinear systems with time-varying output constraints

This paper presents output tracking control for strict feedback nonlinear systems with time-varying output constraint. A Barrier Lyapunov Function (BLF), which depends explicitly on time, is employed at the outset to prevent the output from violating the time-varying constraint. Specifically, we allow the barrier limit to vary with the desired trajectory in time. Through a change of coordinates for the tracking error, we then eliminate the time dependence, therefore simplifying the analysis. We show that asymptotic output tracking is achieved without violation of the time-varying constraint, and that all closed loop signals remain bounded. The performance of the proposed control is illustrated through a simulation example.

Control of fully actuated ocean surface vessels using a class of feedforward approximators

In this brief, we consider the problem of tracking a desired trajectory for fully actuated ocean vessels, in the presence of uncertainties and unknown disturbances. The combination of approximation-based and domination design techniques allows us to handle time-varying disturbances, without the need for explicit knowledge of the bounds. Using backstepping and Lyapunov synthesis, the stable tracking controller is first designed for the full-state feedback case. Subsequently, the output feedback problem is tackled by employing a high-gain observer to estimate the unmeasurable states required by the stable tracking controller. Under the proposed control, semiglobal uniform boundedness of the closed-loop signals is guaranteed for both full-state and output feedback cases.

Adaptive Control of Electrostatic Microactuators With Bidirectional Drive

In this paper, adaptive control is presented for a class of single-degree-of-freedom (1DOF) electrostatic microactuator systems which can be actively driven bidirectionally. The control objective is to track a reference trajectory within the air gap without knowledge of the plant parameters. Both full-state feedback and output feedback schemes are developed, the latter being motivated by practical difficulties in measuring velocity of the moving plate. For the full-state feedback scheme, the system is transformed to the parametric strict feedback form, for which adaptive backstepping is performed to achieve asymptotic output tracking. Analogously, the output feedback design involved transformation to the parametric output feedback form, followed by the use of adaptive observer backstepping to achieve asymptotic output tracking. To prevent contact between the movable and fixed electrodes, special barrier functions are employed in Lyapunov synthesis. All closed-loop signals are ensured to be bounded. Extensive simulation studies illustrate the performance of the proposed control.

Adaptive Neural Network Control for Helicopters in Vertical Flight

In this brief, robust adaptive neural network (NN) control is presented for helicopters in vertical flight, with dynamics in single-input-single-output (SISO) nonlinear nonaffine form. Based on the use of the implicit function theorem and the mean value theorem, we propose a constructive approach for adaptive NN control design with guaranteed stability. Considering both full-state and output feedback cases, it is shown that the output tracking error converges to a small neighborhood of the origin, while the remaining closed-loop signals remain bounded. The simulation study demonstrates the effectiveness of the proposed control.

Control of nonlinear systems with full state constraint using a Barrier Lyapunov Function

This paper presents a control for state-constrained nonlinear systems in strict feedback form to achieve output tracking. To prevent states from violating the constraints, we employ a Barrier Lyapunov Function, which grows to infinity whenever its arguments approaches some limits. By ensuring boundedness of the Barrier Lyapunov Function in the closed loop, we guarantee that the limits are not transgressed.We show that asymptotic output tracking is achieved without violation of state constraints, and that all closed loop signals are bounded, provided that some feasibility conditions on the initial states and control parameters are satisfied. Sufficient conditions to ensure feasibility are provided, and they can be checked offline by solving a static constrained optimization problem. The performance of the proposed control is illustrated through a simulation example.

Control of state-constrained nonlinear systems using Integral Barrier Lyapunov Functionals

This paper presents a control design for nonlinear systems with state constraints, based on the use of our newly introduced Integral Barrier Lyapunov Functionals (iBLF). The integral functional allow the mixing of the original state constraints with the errors in a form amenable to stable backstepping control design. This reduces some of the conservatism associated with the use of purely error-based functions with transformed error constraints. We show that, under the proposed iBLF-based control, output tracking error is bounded by an exponentially decreasing function of time, all states always remain in the constrained state space, and that the stabilizing functions and control input are bounded, subject to significantly relaxed feasibility conditions. A numerical example illustrates the performance of the proposed control.

Continuous Role Adaptation for Human–Robot Shared Control

In this paper, we propose a role adaptation method for human-robot shared control. Game theory is employed for fundamental analysis of this two-agent system. An adaptation law is developed such that the robot is able to adjust its own role according to the humans intention to lead or follow, which is inferred through the measured interaction force. In the absence of human interaction forces, the adaptive scheme allows the robot to take the lead and complete the task by itself. On the other hand, when the human persistently exerts strong forces that signal an unambiguous intent to lead, the robot yields and becomes the follower. Additionally, the full spectrum of mixed roles between these extreme scenarios is afforded by continuous online update of the control that is shared between both agents. Theoretical analysis shows that the resulting shared control is optimal with respect to a two-agent coordination game. Experimental results illustrate better overall performance, in terms of both error and effort, compared with fixed-role interactions.