Tengfei Liu

Distributed formation control of nonholonomic mobile robots without global position measurements

This paper proposes a new class of distributed nonlinear controllers for leader-following formation control of unicycle robots without global position measurements. Nonlinear small-gain design methods are used to deal with the problem caused by the nonholonomic constraint of the unicycle robot and yield simple conditions for practical implementation. With the proposed distributed controllers, the formation control objective can be achieved without assuming any tree sensing structures. More interestingly, the distributed controller is robust to position measurement errors and the linear velocities of the robots can be restricted to specific bounded ranges.

Lyapunov formulation of ISS cyclic-small-gain in continuous-time dynamical networks

This paper provides a Lyapunov formulation of the cyclic-small-gain theorem for general dynamical networks (large-scale systems) composed of continuous-time input-to-state stable (ISS) subsystems. ISS-Lyapunov functions for continuous-time dynamical networks satisfying cyclic-small-gain conditions are constructed from the ISS-Lyapunov functions of the subsystems.

Distributed Output-Feedback Control of Nonlinear Multi-Agent Systems

This technical note presents a cyclic-small-gain approach to distributed output-feedback control of nonlinear multi-agent systems. Through novel distributed observer and control law designs, the closed-loop multi-agent system is transformed into a large-scale system composed of input-to-output stable (IOS) subsystems, the IOS gains of which can be appropriately designed. By guaranteeing the IOS of the closed-loop multi-agent system with the recently developed cyclic-small-gain theorem, the outputs of the controlled agents can be driven to within an arbitrarily small neighborhood of the desired agreement value under bounded external disturbances. Moreover, if the system is disturbance-free, then asymptotic convergence can be achieved. Interestingly, the closed-loop distributed system is also robust to bounded time-delays of exchanged information.

Brief paper: A sector bound approach to feedback control of nonlinear systems with state quantization

This paper studies the feedback control problem of nonlinear systems in strict-feedback form with state quantizers, which are static and bounded by sectors. Through a novel set-valued map based recursive control design approach, the quantized control system is transformed into an interconnection of several input-to-state stable (ISS) subsystems. The ISS property of the closed-loop system is guaranteed by the recently developed cyclic-small-gain theorem. With an appropriately designed quantized controller, the output of the quantized control system can be steered to within a neighborhood of the origin with its size slightly larger than the quantization error near the origin.

A Small-Gain Approach to Robust Event-Triggered Control of Nonlinear Systems

This paper presents a new approach to event-triggered control for nonlinear uncertain systems by using the notion of input-to-state stability (ISS) and the nonlinear small-gain theorem. The contribution of this paper is threefold. First, it is proved that infinitely fast sampling can be avoided if the system is input-to-state stabilizable with the sampling error as the external input and the corresponding ISS gain is locally Lipschitz. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by using ISS small-gain arguments. Second, the proposed approach gives rise to a new self-triggered sampling strategy for a class of nonlinear systems subject to external disturbances. If an upper bound of the external disturbance is known, then the closed-loop system can be designed to be robust to the external disturbance, and moreover, the system state globally asymptotically converges to the origin if the external disturbance decays to zero. Third, a new design method is developed for event-triggered control of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the sampling error as the input can be designed to satisfy the proposed condition for event-triggered control and self-triggered control.

Small-Gain Based Output-Feedback Controller Design for a Class of Nonlinear Systems With Actuator Dynamic Quantization

This technical note presents a novel recursive design approach for output-feedback control of a class of nonlinear systems with actuator quantization. The recently developed cyclic-small-gain theorem is employed to guarantee the input-to-state stability (ISS) of the closed-loop system, along with the construction of an ISS-Lyapunov function. Actuator dynamic quantization is designed based on the ISS-Lyapunov function.

Learning from neural control of nonlinear systems in normal form

A deterministic learning theory was recently proposed which states that an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of simple nonlinear systems. In this paper, we investigate deterministic learning from adaptive neural control (ANC) of a class of nonlinear systems in normal form with unknown affine terms. The existence of the unknown affine terms makes it difficult to achieve learning by using previous methods. To overcome the difficulties, firstly, an extension of a recent result is presented on stability analysis of linear time-varying (LTV) systems. Then, with a state transformation, the closed-loop control system is transformed into a LTV form for which exponential stability can be guaranteed when a partial persistent excitation (PE) condition is satisfied. Accurate approximation of the closed-loop control system dynamics is achieved in a local region along a recurrent orbit of closed-loop signals. Consequently, learning of control system dynamics (i.e. closed-loop identification) from adaptive neural control of nonlinear systems with unknown affine terms is implemented.

Event-based control of nonlinear systems with partial state and output feedback

This paper studies the event-triggered control problem for nonlinear systems with partial state and output feedback. We first consider the control systems that are transformable into an interconnection of two input-to-state stable (ISS) subsystems with the sampling error as the external input. It is shown that infinitely fast sampling can be avoided and asymptotic stabilization can be achieved by appropriately choosing the decreasing rate of the threshold signal of the event-trigger. Then, we focus on the event-triggered output-feedback control problem for nonlinear uncertain systems in the output-feedback form. The key idea is to introduce a novel nonlinear observer-based control design and to transform the control system into the form of interconnected ISS systems. ISS small-gain methods are used as a fundamental tool in the discussions.

Learning From ISS-Modular Adaptive NN Control of Nonlinear Strict-Feedback Systems

This paper studies learning from adaptive neural control (ANC) for a class of nonlinear strict-feedback systems with unknown affine terms. To achieve the purpose of learning, a simple input-to-state stability (ISS) modular ANC method is first presented to ensure the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in finite time. Subsequently, it is proven that learning with the proposed stable ISS-modular ANC can be achieved. The cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using existing methods. To overcome these difficulties, the stable closed-loop system in the control process is decomposed into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation condition for the radial basis function neural network (NN) is established, which guarantees exponential stability of LTV perturbed subsystems. Consequently, accurate approximation of the closed-loop system dynamics is achieved in a local region along recurrent orbits of closed-loop signals, and learning is implemented during a closed-loop feedback control process. The learned knowledge is reused to achieve stability and an improved performance, thereby avoiding the tremendous repeated training process of NNs. Simulation studies are given to demonstrate the effectiveness of the proposed method.

Distributed nonlinear control of mobile autonomous multi-agents

Abstract This paper studies the distributed nonlinear control of mobile autonomous agents with variable and directed topology. A new distributed nonlinear design scheme is presented for multi-agent systems modeled by double-integrators. With the new design, the outputs of the controlled agents asymptotically converge to each other, as long as a mild connectivity condition is satisfied. Moreover, the velocity (derivative of the output) of each agent can be restricted to be within any specified neighborhood of the origin, which is of practical interest for systems under such physical constraint. The new design is still valid if one of the agents is a leader and the control objective is to achieve leader-following. As an illustration of the generality and effectiveness of the presented methodology, the formation control of a group of unicycle mobile robots with nonholonomic constraints is revisited. Instead of assuming the point-robot model, the unicycle model is transformed into two double-integrators by dynamic feedback linearization, and the proposed distributed nonlinear design method is used to overcome the singularity problem caused by the nonholonomic constraint by properly restricting the velocities. Simulation results are included to illustrate the theoretical results.