Justin R. Klotz

Concurrent learning-based approximate feedback-Nash equilibrium solution of N-player nonzero-sum differential games

This paper presents a concurrent learning-based actor-critic-identifier architecture to obtain an approximate feedback-Nash equilibrium solution to an infinite horizon N-player nonzero-sum differential game. The solution is obtained online for a nonlinear control-affine system with uncertain linearly parameterized drift dynamics. It is shown that under a condition milder than persistence of excitation (PE), uniformly ultimately bounded convergence of the developed control policies to the feedback-Nash equilibrium policies can be established. Simulation results are presented to demonstrate the performance of the developed technique without an added excitation signal.

Lyapunov-based robust adaptive control of a quadrotor UAV in the presence of modeling uncertainties

This paper presents the development of a robust adaptive controller for the dynamics of a quadrotor unmanned aerial vehicle (UAV) in the presence of linear-in-the-parameter uncertainties and bounded exogenous disturbances. The controller is designed to asymptotically track a desired position and yaw angle trajectory via a modular adaptive update law and a robust integral sign of the error (RISE) feedback term. A Lyapunov-based stability analysis is used to prove asymptotic tracking of the desired states and to ensure all closed-loop signals remain bounded.

Asymptotic Synchronization of a Leader-Follower Network of Uncertain Euler-Lagrange Systems

This paper investigates the synchronization of a network of Euler-Lagrange systems with leader tracking. The Euler-Lagrange systems are heterogeneous and uncertain and contain bounded, exogenous disturbances. Network communication is governed by an undirected topology. The network leader has a time-varying trajectory which is known to only a subset of the follower agents. A Robust Integral Sign of the Error (RISE) based decentralized control law is developed to guarantee semi-global asymptotic agent synchronization and leader tracking.

Containment control for a social network with state-dependent connectivity

Social interactions influence our thoughts, opinions and actions. In this paper, social interactions are studied within a group of individuals composed of influential social leaders and followers. Each person is assumed to maintain a social state, which can be an emotional state or an opinion. Followers update their social states based on the states of local neighbors, while social leaders maintain a constant desired state. Social interactions are modeled as a general directed graph where each directed edge represents an influence from one person to another. Motivated by the non-local property of fractional-order systems, the social response of individuals in the network are modeled by fractional-order dynamics whose states depend on influences from local neighbors and past experiences. A decentralized influence method is then developed to maintain existing social influence between individuals (i.e., without isolating peers in the group) and to influence the social group to a common desired state (i.e., within a convex hull spanned by social leaders). Mittag-Leffler stability methods are used to prove the asymptotic convergence of the networked fractional-order system.

Ensuring network connectivity for nonholonomic robots during decentralized rendezvous

In a multi-robot system, robots are typically required to collaborate over a communication network to achieve objectives cooperatively. Due to the limited communication and sensing capabilities on each robot, the cooperative objective must be accomplished while ensuring that specified robots stay within each others sensing and communication ranges and that the overall network remains connected. In this paper, a dipolar navigation function and corresponding time-varying continuous controller is developed for repositioning and reorienting a group of wheeled robots with nonholonomic constraints. Only local sensing feedback information from neighbors is used to navigate the robots and maintain network connectivity, which indicates that communication is available when required for various tasks, but communication is not required for navigation. Simulation results demonstrate the performance of the developed approach.

An Adaptive Backstepping Controller for a Hypersonic Air-Breathing Missile

This paper presents the development of an adaptive controller for a hypersonic air-breathing missile with terminal constraints. The controller is designed to regulate the longitudinal dynamics of a hypersonic vehicle model via a backstepping approach. The backstepping approach is used to compensate for uncertainties in the dynamics that do not satisfy the matching condition while ensuring asymptotic tracking of a desired velocity profile and asymptotic regulation of the vehicle position, angle of attack, body angle, and angular rates. A Lyapunov-based stability analysis is used to prove the asymptotic regulation of the controlled states. Simulation results are presented to verify the performance of the controller.

Unknown time-varying input delay compensation for uncertain nonlinear systems ☆

Abstract A tracking controller is developed for a class of uncertain nonlinear systems subject to unknown time-varying input delay and additive disturbances. A novel filtered error signal is designed using the past states in a finite integral over a constant estimated delay interval. The maximum tolerable error between unknown time-varying delay and a constant estimate of the delay is determined to establish uniformly ultimately bounded convergence of the tracking error to the origin. The controller development is based on an approach which uses Lyapunov–Krasovskii functionals to analyze the effects of unknown sufficiently slowly time-varying input delays. A stability analysis is provided to prove ultimate boundedness of the tracking error signals. Numerical simulation results illustrate the performance of the developed robust controller.

Containment control for a directed social network with state-dependent connectivity

Social interactions influence our thoughts, opinions and actions. In this paper, social interactions are studied within a group of individuals composed of influential social leaders and follower groupies. Each person is assumed to maintain a social state, which can be an emotional state or an opinion on a social event. Followers update their own states based on the states of local neighbors, which are considered as reasonable, while the social leaders maintain a desired constant state. Social interactions are modeled as a directed graph where each directed edge represents an influence from one person to another. Motivated by the non-local property of fractional-order systems, the social response of individuals in the network are modeled by fractional-order dynamics whose states depend on influences from local neighbors and past experiences. A decentralized influence method is then developed to maintain existing social influence between individuals (i.e., without isolating peers in the group), and to influence the social group to a common desired state (i.e., within a convex hull spanned by social leaders). Mittag-Leffler stability methods are used to prove asymptotic stability of the networked fractional-order system.

Event-Triggered Control of Multiagent Systems for Fixed and Time-Varying Network Topologies

A decentralized controller that uses event-triggered communication scheduling is developed for the leader-follower consensus problem under fixed and switching communication topologies. To eliminate continuous interagent communication, state estimates of neighboring agents are designed for control feedback and are updated via communication to reset growing estimate errors. The communication times are based on an event-triggered approach and are adapted based on the trade-off between the control system performance and the desire to minimize the amount of communication. An important aspect of the developed event trigger strategy is that communication is not required to determine when a state update is needed. Since the control strategy produces switched dynamics, analysis is provided to show that Zeno behavior is avoided by developing a positive constant lower bound on the minimum inter-event interval. A Lyapunov-based convergence analysis is also provided to indicate bounded convergence of the developed control methodology.

Asymptotic synchronization of leader-follower networks of uncertain Euler-Lagrange systems

This paper investigates the synchronization of a network of Euler-Lagrange systems with leader tracking. The Euler-Lagrange systems are heterogeneous and uncertain and contain bounded, exogenous disturbances. The network leader has a time-varying trajectory which is known to only a subset of the follower agents. A robust integral sign of the error-based decentralized control law is developed to yield semiglobal asymptotic agent synchronization and leader tracking.