Exogenous Disturbances Research Articles

Regret optimal control for uncertain stochastic systems

We consider control of uncertain linear time-varying stochastic systems from the perspective of regret minimization. Specifically, we focus on the problem of designing a feedback controller that minimizes the loss relative to a clairvoyant optimal policy that has foreknowledge of both the system dynamics and the exogenous disturbances. In this competitive framework, establishing robustness guarantees proves challenging as, differently from the case where the model is known, the clairvoyant optimal policy is not only inapplicable, but also impossible to compute without knowledge of the system parameters. To address this challenge, we embrace a scenario optimization approach, and we propose minimizing regret robustly over a finite set of randomly sampled system parameters. We prove that this policy optimization problem can be solved through semidefinite programming, and that the corresponding solution retains strong probabilistic out-of-sample regret guarantees in face of the uncertain dynamics. Our method naturally extends to include satisfaction of safety constraints with high probability. We validate our theoretical results and showcase the potential of our approach by means of numerical simulations.

Nonfragile Filtering under Bounded Exogenous Disturbances

Nonfragile Filtering under Bounded Exogenous Disturbances

Nonfragile Filtering under Bounded Exogenous Disturbances

Nonfragile Filtering under Bounded Exogenous Disturbances

Fractional-order super-twisting sliding mode attitude control for elastic refueling boom with exogenous disturbances

Fractional-order super-twisting sliding mode attitude control for elastic refueling boom with exogenous disturbances

Accelerated Gradient Approach For Deep Neural Network-Based Adaptive Control of Unknown Nonlinear Systems.

Recent connections in the adaptive control literature to continuous-time analogs of Nesterov's accelerated gradient method have led to the development of new real-time adaptation laws based on accelerated gradient methods. However, previous results assume that the system's uncertainties are linear-in-the-parameters (LIP). To compensate for non-LIP uncertainties, our preliminary results developed a neural network (NN)-based accelerated gradient adaptive controller to achieve trajectory tracking for nonlinear systems; however, the development and analysis only considered single-hidden-layer NNs. In this article, a generalized deep NN (DNN) architecture with an arbitrary number of hidden layers is considered, and a new DNN-based accelerated gradient adaptation scheme is developed to generate estimates of all the DNN weights in real-time. A nonsmooth Lyapunov-based analysis is used to guarantee the developed accelerated gradient-based DNN adaptation design achieves global asymptotic tracking error convergence for general nonlinear control affine systems subject to unknown (non-LIP) drift dynamics and exogenous disturbances. A comprehensive set of simulation studies are conducted on a two-state nonlinear system, a robotic manipulator, and a complex 20-D nonlinear system to demonstrate the improved performance of the developed method. Our simulation studies demonstrate enhanced tracking and function approximation performance from both DNN architectures and accelerated gradient adaptation.

Rapid Approximation of Low-Thrust Spacecraft Reachable Sets within Complex Two-Body and Cislunar Dynamics

The reachable set of controlled dynamical systems is the set of all reachable states from an initial condition over a certain time horizon, subject to operational constraints and exogenous disturbances. In astrodynamics, rapid approximation of reachable sets is invaluable for trajectory planning, collision avoidance, and ensuring safe and optimal performance in complex dynamics. Leveraging the connection between minimum-time trajectories and the boundary of reachable sets, we propose a sampling-based method for rapid and efficient approximation of reachable sets for finite- and low-thrust spacecraft. The proposed method combines a minimum-time multi-stage indirect formulation with the celebrated primer vector theory. Reachable sets are generated under two-body and circular restricted three-body (CR3B) dynamics. For the two-body dynamics, reachable sets are generated for (1) the heliocentric phase of a benchmark Earth-to-Mars problem, (2) two scenarios with uncertainties in the initial position and velocity of the spacecraft at the time of departure from Earth, and (3) a scenario with a bounded single impulse at the time of departure from Earth. For the CR3B dynamics, several cislunar applications are considered, including L1 Halo orbit, L2 Halo orbit, and Lunar Gateway 9:2 NRHO. The results indicate that low-thrust spacecraft reachable sets coincide with invariant manifolds existing in multi-body dynamical environments. The proposed method serves as a valuable tool for qualitatively analyzing the evolution of reachable sets under complex dynamics, which would otherwise be either incoherent with existing grid-based reachability approaches or computationally intractable with a complete Hamilton–Jacobi–Bellman method.

Robust internal models with a star-shaped attractor are linear

In linear regulation theory, it is well-known that embedding in the control loop a suitable internal model of the exogenous disturbances and references permits to achieve perfect regulation of the desired variables robustly with respect to parametric uncertainties in the plant’s equations. However, it was recently proved that this principle does not extend, in general, to nonlinear systems or non-parametric perturbations. Indeed, there exist systems for which no smooth finite-dimensional regulator can exist that regulates the desired variables to zero in spite of unstructured uncertainties affecting the plant’s dynamics. This article complements such a negative result by proving that, in the canonical context of minimum-phase normal forms, a nonlinear regulator of the Luenberger type that guarantees robust asymptotic regulation with respect to unstructured uncertainties and possesses a star-shaped attractor necessarily behaves as a linear system on such an attractor. This result further strengthens the conjecture that robust regulation is essentially a linear property.

Adaptive fast trajectory tracking control for the airship based on prescribed performance

A fast trajectory tracking controller is designed for the airship, involving dynamic uncertainties of parameters, capable of guaranteeing the prescribed performance of tracking errors, and fast response of the closed-loop system. To achieve the decoupling of velocity control and attitude control of the airship, a new guidance and control integration framework is proposed first. Then, based on the dynamics model established by the spinor method, the lumped disturbance, caused by unknown aerodynamic parameter uncertainties and exogenous disturbances, is estimated online using a high-order finite-time observer. The control performance, namely, overshoot and steady-state performance of tracking errors, is significantly improved by utilizing the prescribed output performance constraints, while the convergence rate is further enhanced by combining the finite-time convergence property of the fast terminal sliding mode control. Simulation results attest to the effectiveness of the strategy in this paper. Compared with the adaptive fast terminal sliding mode control, the strategy effectively utilizes the capability of the actuator within the allowed range and reduces the convergence time by more than half with similar control inputs.

Nonlinear disturbance observer-based geometric attitude fault-tolerant control of quadrotors

This paper is concerned with nonlinear disturbance observer (DO)-based geometric attitude fault-tolerant control (FTC) problem of quadrotor unmanned aerial vehicles (UAVs) subject to system uncertainties, exogenous disturbances, and actuator faults. A disturbance observer-based control (DOBC) framework is devised to tackle the difficulties caused by system uncertainties and external disturbances. The FTC is proposed to cope with the occurrence of actuator faults which can be modelled as a constant loss of effectiveness. The proposed design scheme can provide an effective way to analyse the stability of the closed-loop system, which can ensure the asymptotical convergence of the error. The other method considers actuator failures as part of the lumped disturbance, and the attitude tracking problem of quadrotors concerning the lumped disturbance is solved by the DO-based control method, which can ensure the exponential convergence of the error. The numerical simulations are performed to illustrate the effectiveness of the design techniques.

Integral Sliding Mode Disturbance Observer-Based Preview Repetitive Control

Abstract This paper deals with the problem of integral sliding mode disturbance observer (ISDOB)-based preview repetitive control (PRC) for a class of nonlinear systems subject to external disturbances and nonlinearity. First, an ISDOB-based PRC law is presented to estimate and compensate the exogenous disturbances and nonlinearity. Next, by using a new equality constraint, a continuous-discrete two-dimensional (2D) system is established. Then, the stability of the combined controller–observer system is derived on the basis of a Lyapunov analysis, 2D system theory, and the singular-value-decomposition technique. By solving an linear matrix inequality (LMI), the gains of the controller and state observer can be obtained. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of the proposed method.

Mechanisms of microbial coexistence in a patchy ecosystem: Differences in ecological niche overlap and species fitness between rhythmic and non-rhythmic species

Resource patchiness caused by external events breaks the continuity and homogeneity of resource distribution in the original ecosystem. For local organisms, this leads to drastic changes in the availability of resources, breaks down the co-existence of species, and reshuffles the local ecosystem. West Lake is a freshwater lake with resource patchiness caused by multiple exogenous disturbances that has strong environmental heterogeneity that prevents clear observation of seasonal changes in the microbial communities. Despite this, the emergence of rhythmic species in response to irregular changes in the environment has been helpful for observing microbial communities dynamics in patchy ecosystems. We investigated the ecological mechanisms of seasonal changes in microbial communities in West Lake by screening rhythmic species based on the ecological niche and modern coexistence theories. The results showed that rhythmic species were the dominant factors in microbial community changes and the effects of most environmental factors on the microbial community were indirectly realised through the rhythmic species. Random forest analyses showed that seasonal changes in the microbial community were similarly predicted by the rhythmic species. In addition, we incorporated species interactions and community phylogenetic patterns into stepwise multiple regression analyses, the results of which indicate that ecological niches and species fitness may drive the coexistence of these subcommunities. Thus, this study extends our understanding of seasonal changes in microbial communities and provides new ways for observing seasonal changes in microbial communities, especially in ecosystems with resource patches. Our study also show that combining community phylogenies with co-occurrence networks based on ecological niches and modern coexistence theory can further help us understand the ecological mechanisms of interspecies coexistence.

Adaptive optimal control system design for semi-active suspension system by supposing variable parameters under exogenous road disturbance

Adaptive optimal control system design for semi-active suspension system by supposing variable parameters under exogenous road disturbance

Geometric prescribed‐time control of quadrotors with adaptive extended state observers

AbstractThis article studies an adaptive extended state observer (AESO) based prescribed‐time geometric attitude stabilization problem of quadrotors with endogenous uncertainties, exogenous disturbances, and actuator saturation, which can be estimated and compensated by AESOs. The employment of the geometric representation method for system attitude can effectively avoid ambiguity or singularity problems that may arise with other representations. The temporal and scale transformations are employed to solve the global boundedness problem on infinite time instead of the prescribed‐time convergence problem on finite time. By integrating the proposed controller with the backstepping technique, the system of quadrotors can be prescribed‐time stable. Further, a prescribed‐time geometric attitude control technique is devised such that the control signal is bounded and the state signals converge to a small domain near the equilibrium point in the prescribed time. The prescribed time is determined by the user and is independent of the initial conditions. The comparative simulations with different initial information are performed to demonstrate the effectiveness of the proposed design technique.

Rotary inverted pendulum control using neuro-adaptive robust generalized dynamic inversion

The objective of this research is to design a robust control system for trajectory tracking of the under-actuated Rotary Inverted Pendulum (RIP). The focus is on achieving semi-global asymptotic stability in the absence of knowledge about the RIP geometric and inertia parameters. The control design commences by formulating differential servo constraint dynamics (VCD) that encapsulates the control objectives for the RIP. The baseline generalized dynamic inversion (GDI) control law is derived by inverting the VCD for the control voltage input using the Moore–Penrose generalized inverse. To enhance robustness against modeling uncertainties and exogenous disturbances, a sliding mode control (SMC) element is integrated within the GDI control system, resulting in the robust GDI (RGDI) control system. Furthermore, an adaptive estimator that is based on Radial Basis Function Neural Networks (RBF-NN) is adopted to eliminate the dependency of the RGDI control system on the RIP mathematical model. The weighting matrices of the RBF-NN are updated with the aid of a Lyapunov control function. The proposed control system offers robust solution and guarantees semi-global asymptotic stability to the unstable equilibria of the RIP dynamics in the absence of a mathematical model. The proposed control system’s performance is evaluated through computer simulations and experimental tests on a real RIP system. Comparative analyses with traditional SMC and linear quadratic control methodologies are conducted to show the effectiveness of the proposed approach.

Finite-Time Fault-Tolerant Formation Control for Distributed Multi-Vehicle Networks With Bearing Measurements

This paper addresses a bearing-only formation tracking problem in robotic networks by considering exogenous disturbances and actuator faults. In contrast to traditional position-based coordination strategies, the bearing-only coordinated movements of the unmanned vehicles only rely on the neighboring bearing information. This feature can be utilized to reduce the sensing requirements in the hardware implementation. A gradient-descent protocol is first developed to achieve the desired coordination within a prespecified settling time, where the unknown disturbances are considered in the vehicle dynamics, then the bound of formation tracking error is guaranteed by the Lyapunov approach. In case of damage to the actuators (e.g., motors) in some of the vehicles during the task, fault-tolerant analysis of the proposed controller is provided to ensure the success of the task in extreme environments. Furthermore, the proposed bearing-based method is extended to deal with general linear systems, which can be applied to a wider range of robotic platforms. Finally, numerical simulations and lab-based experiments using unmanned ground vehicles are conducted to validate the effectiveness of the proposed strategy. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The aim of this paper is to develop and design a practical bearing-only formation control approach for multi-vehicle systems. Many real-world complex tasks can be solved by multiple unmanned aerial and ground vehicles being connected by a communication network. This paper has proposed a formation tracking scheme for networked multi-vehicle systems that only relies on the relative bearing information of the neighboring vehicles. Closed-loop stability of the scheme and finite-time convergence of the tracking error have been established using the Lyapunov stability approach. The proposed method ensures the robustness and fault-tolerance of the multi-vehicle system against hardware faults or exogenous disturbances. A systematic set of guidelines on how to apply the proposed strategy in practice is also provided for the control practitioners in the form of an algorithm. In order to demonstrate the feasibility and usefulness of the proposed coordination scheme, numerical simulations and lab-based hardware experiments were conducted. Potential applications of the proposed scheme include search and rescue, security surveillance and cooperative exploration.

Reliability-based anti-disturbance control for systems with parametric stochastic uncertainty: A probabilistic LMI approach

We propose a reliability-based anti-disturbance control (RADC) method for systems with parametric stochastic uncertainty based on the linear matrix inequality (LMI) and the limit state function. Differing from the existing anti-disturbance control, the parametric stochastic uncertainty is considered in both the concerned system and the exogenous disturbance system. With this consideration, the condition for system stability and performance robustness is described by a stochastic LMI which holds with a certain probability (reliability). Through the limit state function method, the stochastic LMI is subtly transformed into two probabilistic LMIs for two different cases. The proposed probabilistic LMIs contain two probabilistic parameters of reliability indexes that quantify the effect of parametric stochastic uncertainty. At different prescribed reliability indexes, controllers with different reliability can be flexibly and reliably designed. Two illustrative examples with Monte-Carlo verification are presented to demonstrate the feasibility and effectiveness of the proposed RADC method.

Equivalent Input Disturbance-Based Control: Analysis, Development, and Applications.

This article reviews the concept, analysis, development, and applications of the equivalent-input-disturbance (EID) approach. First, the definition and existence of the EID are given, and the configuration of the EID estimator is provided. Next, estimation errors in the conventional EID approach are explained, and error-suppression methods are exhibited, which improve the disturbance-rejection performance. Then, this article describes how to apply the EID approach and associate challenges in dealing with nonlinearities, time delays, and uncertainties. Moreover, this article reviews some additional meaningful studies that cannot be categorized into the above-mentioned classes. Finally, some conclusions and future directions are given. The EID approach has been successfully used to suppress the influences of exogenous disturbances, nonlinearities, time delays, and uncertainties in many control systems to improve control performance and robustness. Studies can further rich the theory of the EID approach in the future, such as designing evaluation index, improving disturbance-rejection performance, developing new applications, and combining with other control theory.

Event-Triggered Impulsive Control for Input-to-State Stabilization of Nonlinear Time-Delay Systems.

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.

A Direct Adaptive Controller With Harmonic Compensation for Grid-Connected Converters

Grid-connected converters are uncertain time-varying systems, whose controllers must deal with the relevant inductive content and high harmonic distortion of the sampled voltages. Adaptive controllers are feasible control strategies for these applications, because their gains are continuously adjusted in response to system perturbations, and they are also robust to unmodeled dynamics and exogenous disturbances. However, adaptive controllers are not necessarily capable of rejecting all harmonic components on grids with high harmonic distortion. Therefore, this work presents a Robust Model Reference Adaptive Control-based with an adaptive super-twisting sliding mode, which is improved with a harmonic compensation strategy in which additional control actions to deal with the harmonic contents of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5^{th}$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$7^{th}$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$11^{th}$</tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$13^{th}$</tex-math></inline-formula> of the fundamental component of the electrical grid are incorporated into the control structure. Experimental results are provided of a 7.5 kW converter connected to a distorted and unbalanced grid with an LCL filter, where the developed control structure presents a total harmonic distortion (THD) of 2%, while the controller without harmonic compensation obtains a 2.5% THD.

Periodic and Dynamic Periodic Event-Triggered Control for Nonlinear Cyber-Physical Systems Under DoS Attacks via a Hybrid System Approach

This paper is focused on the problem of periodic and dynamic periodic event-triggered control for nonlinear cyber-physical systems (CPSs) under denial-of-service (DoS) attacks and exogenous disturbances. The analysis relies on a new model to design periodic event-triggered control and dynamic periodic event-triggered control schemes such that the nonlinear CPSs are resilient to a class of malicious attacks which can be characterized by attacking frequency and attacking duration. By developing an average dwell-time automaton and a time-ratio monitor to describe frequency and duration of the DoS attacks, general hybrid dynamical frameworks are firstly proposed for event-triggered nonlinear CPSs. Based on the established models, novel Lyapunov functions are constructed. Furthermore, thanks to the Lyapunov-based approach, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> -gain performance of the considered nonlinear CPSs under DoS attacks is analyzed. Finally, the feasibility of the theoretical findings is demonstrated by a numerical example.