This paper presents a tracking controller for nonlinear systems with matched uncertainties based on contraction metrics and disturbance estimation that provides exponential convergence guarantees. ...Within the proposed approach, a disturbance estimator is proposed to estimate the pointwise value of the uncertainties, with a pre-computable estimation error bounds (EEB). The estimated disturbance and the EEB are then incorporated in a robust Riemannian energy condition to compute the control law that guarantees exponential convergence of actual state trajectories to desired ones. Simulation results on aircraft and planar quadrotor systems demonstrate the efficacy of the proposed controller, which yields better tracking performance than existing controllers for both systems.
In recent years, the increasing popularity of multi-vehicle missions has been accompanied by a growing interest in the development of control strategies to ensure safety in these scenarios. In this ...work, we propose a control framework for coordination and collision avoidance in cooperative multi-vehicle missions based on a speed adjustment approach. The overall problem is decoupled in a coordination problem, in order to ensure coordination and inter-vehicle safety among the agents, and a collision-avoidance problem to guarantee the avoidance of non-cooperative moving obstacles. We model the network over which the cooperative vehicles communicate using tools from graph theory, and take communication losses and time delays into account. Finally, through a rigorous Lyapunov analysis, we provide performance bounds and demonstrate the efficacy of the algorithms with numerical and experimental results.
Bernstein polynomial approximation of continuous function has a slower rate of convergence compared to other approximation methods. “The fact seems to have precluded any numerical application of ...Bernstein polynomials from having been made. Perhaps they will find application when the properties of the approximant in the large are of more importance than the closeness of the approximation.”—remarked P.J. Davis in his 1963 book, Interpolation and Approximation. This paper presents a direct approximation method for nonlinear optimal control problems with mixed input and state constraints based on Bernstein polynomial approximation. We provide a rigorous analysis showing that the proposed method yields consistent approximations of time-continuous optimal control problems and can be used for costate estimation of the optimal control problems. This result leads to the formulation of the Covector Mapping Theorem for Bernstein polynomial approximation. Finally, we explore the numerical and geometric properties of Bernstein polynomials, and illustrate the advantages of the proposed approximation method through several numerical examples.
This article presents an adaptive reference governor (RG) framework for a linear system with matched nonlinear uncertainties that can depend on both time and states, subject to both state and input ...constraints. The proposed framework leverages an <inline-formula><tex-math notation="LaTeX">{\mathcal {L}_{1}}</tex-math></inline-formula> adaptive controller (<inline-formula><tex-math notation="LaTeX">{\mathcal {L}_{1}}</tex-math></inline-formula>AC) that compensates for the uncertainties, and provides guaranteed transient performance in terms of uniform bounds on the error between actual states and inputs and those of a nominal (i.e., uncertainty-free) system. The uniform performance bounds provided by the <inline-formula><tex-math notation="LaTeX">{\mathcal {L}_{1}}</tex-math></inline-formula>AC are used to tighten the prespecified state and control constraints. A reference governor is then designed for the nominal system using the tightened constraints, which guarantees robust constraint satisfaction. Moreover, the conservatism introduced by constraint tightening can be systematically reduced by tuning some parameters within the <inline-formula><tex-math notation="LaTeX">{\mathcal {L}_{1}}</tex-math></inline-formula>AC. Compared with existing solutions, the proposed adaptive RG framework can potentially yield reduced conservativeness for constraint enforcement and improved tracking performance due to the inherent uncertainty compensation mechanism. Simulation results for a flight control example illustrate the efficacy of the proposed framework.
Experimental results are presented that illustrate a recently developed method for adaptive output feedback control. The method permits adaptation to both parametric uncertainty and unmodeled ...dynamics, and incorporates a novel approach that permits adaptation under known actuator characteristics including actuator dynamics and saturation. Only knowledge of the relative degree of the controlled system within the bandwidth of the control design is required. The controller design was tested by controlling the pitch axis of a three degrees-of-freedom (DOF) helicopter model, using attitude feedback through a low-resolution optical sensor.
This article studies novel attack and defense strategies, based on a class of stealthy attacks, namely the zero-dynamics attack (ZDA), for multiagent control systems. ZDA poses a formidable security ...challenge since its attack signal is hidden in the null space of the state-space representation of the control system and hence it can evade conventional detection methods. An intuitive defense strategy builds on changing the aforementioned representation via switching through a set of carefully crafted topologies. In this article, we propose realistic ZDA variations where the attacker is aware of this topology-switching strategy, and hence employs the following policies to avoid detection: first, pause, update, and resume ZDA according to the knowledge of switching topologies; and second, cooperate with a concurrent stealthy topology attack that alters network topology at switching times, such that the original ZDA is feasible under the corrupted topology. We first systematically study the proposed ZDA variations, and then develop defense strategies against them under the realistic assumption that the defender has no knowledge of attack starting, pausing, and resuming times and the number of misbehaving agents. Particularly, we characterize conditions for detectability of the proposed ZDA variations, in terms of the network topologies to be maintained, the set of agents to be monitored, and the measurements of the monitored agents that should be extracted, while simultaneously preserving the privacy of the states of the nonmonitored agents. We then propose an attack detection algorithm based on the Luenberger observer, using the characterized detectability conditions. We provide numerical simulation results to demonstrate our theoretical findings.
This article considers adaptive output-feedback control problem for nonsquare multi-input–multi-output systems (MIMO) with arbitrary relative degree. The proposed controller, based on the Formula ...Omitted adaptive control architecture, is designed using the right interactor matrix and a suitably defined projection matrix. A state-output predictor, a low-pass filter, and adaptive laws are introduced that achieve output tracking of a desired reference signal. It is shown that the proposed control strategy guarantees closed-loop stability with arbitrarily small steady-state errors. The transient performance in the presence of nonzero initialization errors is quantified in terms of decreasing functions. Rigorous mathematical analysis and illustrative examples are provided to validate the theoretical claims.
As a systematic method for gain-scheduling, the linear parameter-varying (LPV) system framework has been widely used for the design of aerospace control systems with large operating envelopes. This ...paper presents design and analysis of an adaptive control architecture for LPV systems subject to time-varying parametric uncertainties and external disturbances, with both transient and steady-state performance guarantees. We introduce new tools relying on parameter-dependent Lyapunov functions and linear matrix inequality techniques for stability and performance analysis. These tools – limited to linear systems – potentially yield less conservative results than the approach employed for this architecture in previous adaptive control literature based on the small-gain theorem. The transient and steady-state performance of the adaptive closed-loop system, in terms of input and output signals, is quantified with respect to a non-adaptive reference system that depends on the true values of the uncertainties and represents the best achievable performance. It is shown that the transient performance bounds can be made arbitrarily small in the case of zero initialization error for the state predictor and will include additional exponentially decaying terms in the presence of non-zero initialization error. The approach can be used to design an adaptive augmentation of a baseline LPV control system. A simulation example of the longitudinal dynamics of a conceptual Urban Air Mobility aircraft is used to illustrate the efficacy of the proposed framework.
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