Control Of Dynamic Systems Research Articles

Regret-Optimal Estimation and Control

We consider estimation and control in linear dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal state estimators and causal controllers which compete against a clairvoyant noncausal policy, instead of the best policy selected in hindsight from some fixed parametric class. We show that regret-optimal filters and regret-optimal controllers can be derived in state-space form using operator-theoretic techniques from robust control. Our results can be viewed as extending traditional robust estimation and control, which focuses on minimizing worst-case cost, to minimizing worst-case regret. We propose regret-optimal analogs of Model-Predictive Control (MPC) and the Extended Kalman Filter (EKF) for systems with nonlinear dynamics and present numerical experiments which show that these algorithms can significantly outperform standard approaches to estimation and control.

Composite anti-disturbance control for ship dynamic positioning systems with thruster faults

Anti-disturbance control problem is studied for ship dynamic positioning systems with model uncertainties and ocean disturbances under thruster faults. For the ocean disturbance, a stochastic disturbance observer (SDO) is established to give the online estimation. For thruster faults, an adaptive law is used to evaluate, which is obtain from Lyapunov function. For model uncertainties, a robust control term with adaptive technology is used to attenuate it. Then, a composite anti-disturbance control (CADC) strategy is raised by combining disturbance observer-based control (DOBC), adaptive technology, and robust control term, which makes the position and yaw angle of ship reach the desired values. Finally, the simulation example proves the validity of the controller.

Control of Dynamic Systems under Input and Output Constraints

Control of Dynamic Systems under Input and Output Constraints

Maximum Entropy Optimal Control of Continuous-Time Dynamical Systems

Maximum entropy reinforcement learning methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of the existing techniques are designed for discrete-time systems although there has been a growing interest to handle physical processes evolving in continuous time. As a first step toward their extension to continuous-time systems, this article aims to study the theory of maximum entropy optimal control in continuous time. Applying the dynamic programming principle, we derive a novel class of Hamilton–Jacobi–Bellman (HJB) equations and prove that the optimal value function of the maximum entropy control problem corresponds to the unique viscosity solution of the HJB equation. We further show that the optimal control is uniquely characterized as Gaussian in the case of control-affine systems and that, for linear-quadratic problems, the HJB equation is reduced to a Riccati equation, which can be used to obtain an explicit expression of the optimal control. The results of our numerical experiments demonstrate the performance of our maximum entropy method in continuous-time optimal control and reinforcement learning problems.

Generalization of the thermodynamic approach to multi-dimensional quasistatic processes

A method of mathematical modeling of multidimensional quasi-static processes, a generalization of quasi-static processes of equilibrium thermodynamics, is proposed and substantiated. The authors obtain a generalization of the first and the second law of thermodynamics in the form of Carathéodory to multidimensional quasi-static processes. The idea of generalization is to construct an orthogonal system of functionals similar to the work and heat functionals of classical thermodynamics along families of phase trajectories corresponding to different types of influences on a multidimensional quasi-static system. The representation of quasi-static processes by systems of ordinary differential equations containing control variables is substantiated. The obtained results make it possible to use a wide arsenal of methods of the theory of control of dynamical systems to solve problems of control of quasi-static processes.

Double internal loop higher-order recurrent neural network-based adaptive control of the nonlinear dynamical system

Double internal loop higher-order recurrent neural network-based adaptive control of the nonlinear dynamical system

Implementation of T-S fuzzy approach for the synchronization and stabilization of non-integer-order complex systems with input saturation at a guaranteed cost

One of the fundamental topics in engineering that has many applications in applied sciences is guaranteed cost control and synchronization of chaotic dynamical systems. In this paper, a Takagi–Sugeno (T-S) fuzzy model-free state feedback (MFSF) technique is used to synchronize and stabilize various complex fractional-order systems (FOSs) in the presence of input saturation. A T-S fuzzy MFSF method is developed to suppress the inappropriate behavior of the FOSs without any unpleasant chattering phenomena using the non-integer form of the Lyapunov stability theory (LST) and linear matrix inequality concept. The suggested MFSF technique may be used to stabilize and synchronize FOSs with model uncertainty, external disturbances, and input saturation. The designed method has the advantages of being a model-free technique, being resistant to uncertainties, being simple to use, and achieving the equilibrium point quickly at a guaranteed cost. Furthermore, the effectiveness and application of the T-S fuzzy MFSF are proven using the suggested approach to synchronize two separate canonical chaotic FOSs and stabilize the permanent magnet synchronous motor (PMSM) chaotic system. Two comparisons demonstrate the efficacy and advantages of the T-S fuzzy approach over other existing control methods.

Robust control of vehicle suspension systems with friction non-linearity for ride comfort enhancement

Robust controllers are attracting considerable interest in control of dynamic systems due to their capability of eliminating parameterized or unparameterized uncertainties. Therefore, model based robust control law is proposed in this study for ride comfort enhancement and applied on a 7 degree-of-freedom full-car suspension system with friction non-linearity. Inertia, spring and damping forces of the system are modelled with parameterized uncertainties while friction forces and external disturbances are considered as unmodelled dynamics, namely, unparameterized uncertainties. To better understand the effectiveness of proposed controller, a dry friction model that has non-linear characteristics is used for analysis. Closed-loop stability of the system is achieved by using well-known Lyapunov Stability Theorem. To better evaluate the effect of proposed robust controller on ride comfort enhancement with successful road holding, extensive numerical analysis is performed and the results are compared with those of previous similar controller and passive suspension system. The effectiveness of proposed control method has been confirmed. Consequently, satisfactory results have been obtained proving that the ride comfort of a vehicle that has both parameterized and unparameterized uncertainties has been further improved with reasonable power consumption values for a vehicle in terms of economic viability.

Bounded Partial Pinning Control of Network Dynamical Systems

Controlling collective behavior has been the key goal of researchers both from the engineering and physics communities working in the field of control of network systems. In the literature, pinning control has often emerged as the tool of choice to achieve this task. Only recently, though, has the problem of controlling only a fraction of the network nodes been tackled. Here, we consider the case in which, due to the disturbing influence of an external node, which we identify as an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opponent</i> , the network nodes cannot asymptotically converge to the pinner's trajectory, and only a bounded convergence can be achieved. We derive analytic conditions guaranteeing that all the nodes in a given strongly connected component of the network achieve bounded convergence to the trajectory of the pinner, and provide an estimate of the convergence bound. Finally, we apply our results to an opinion dynamics scenario, showing that a pinned node selection strategy grounded on our theoretical results is effective in steering the opinions of the majority of the network nodes toward that of the pinner.

A Systematic Literature Review on Rapid Control Prototyping Applications

In this paper, a systematic literature review of rapid control prototyping, which facilitates education in the modelling and control of dynamic systems because it reduces programming effort, is presented. Six questions were proposed that were used in the analyses of one hundred references from conference and journal papers. The questions used are, for example, the dates and geographic regions of the publication, software and hardware platforms, differences, similarities, and application areas. Several applications were reviewed in electrical systems, transport vehicles, nonlinear systems, power electronics, process control, industrial automation, and robotics. The review concludes with which geographic regions are more prolific, the advantages and problems of the use of RCP, and what differences exist between the commercial and free software design.

Editorial: Tensor numerical methods and their application in scientific computing and data science

Editorial: Tensor numerical methods and their application in scientific computing and data science

Optimal Control of Dynamical Systems using Calculus of Variations

This paper explores the application of calculus of variations techniques for optimizing the control of complex dynamical systems. Determining control strategies that minimize cost metrics and satisfy constraints is critical across engineering disciplines like robotics, aerospace, and process operations. Classical optimal control methods, such as Pontryagin's Maximum Principle, transform an optimal control problem into a calculus of variations framework amenable to analytical and numerical optimization. We present a unified framework for applying these techniques, enabling dynamical systems defined by ordinary and partial differential equations to be optimized by conversion into a nonlinear programming form. Analytical approaches provide theoretical guarantees on control performance while numerical methods, like direct collocation and transcription, enable large-scale optimal control problems to be efficiently solved. The connections between dynamical systems, calculus of variations, and modern numerical optimization methods establish a holistic methodology for control engineers and applied mathematicians to design optimal controllers for physical systems. Case studies on real-time trajectory optimization, adaptive path planning, and dynamic process operations demonstrate the efficacy of the proposed optimal control framework across robotics, aerospace, power systems, and other applications.

Optimal Control of Dynamical Systems using Calculus of Variations

This paper explores the application of calculus of variations techniques for optimizing the control of complex dynamical systems. Determining control strategies that minimize cost metrics and satisfy constraints is critical across engineering disciplines like robotics, aerospace, and process operations. Classical optimal control methods, such as Pontryagin's Maximum Principle, transform an optimal control problem into a calculus of variations framework amenable to analytical and numerical optimization. We present a unified framework for applying these techniques, enabling dynamical systems defined by ordinary and partial differential equations to be optimized by conversion into a nonlinear programming form. Analytical approaches provide theoretical guarantees on control performance while numerical methods, like direct collocation and transcription, enable large-scale optimal control problems to be efficiently solved. The connections between dynamical systems, calculus of variations, and modern numerical optimization methods establish a holistic methodology for control engineers and applied mathematicians to design optimal controllers for physical systems. Case studies on real-time trajectory optimization, adaptive path planning, and dynamic process operations demonstrate the efficacy of the proposed optimal control framework across robotics, aerospace, power systems, and other applications.

Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.

New Approach to the Synthesis of Optimal Terminal Control of Nonlinear Dynamic Systems

The problem of constructing common solutions to terminal control problems of nonlinear systems is considered here. Previously proven positions are used that the optimal trajectory is an envelope of a parametric family of surfaces (a parametric family of singular curves), and that optimal control can be found on this family. The fact that at each point of the optimal trajectory the vector-function of Lagrange factors is tangent to it, but also tangent to the singular curve, is played out here. A constructive method of constructing singular curves based on conditional separation of variables in the Hamilton-Jacobi equation is given. The " free" parameters of singular curves are based on the condition of minimizing the terminal functionality, which avoids an explicit solution to the boundary problem for a class of nonlinear dynamic systems, and simplifies computational algorithms. Singular curves are described by a reduced (abbreviated) mathematical model. Thus, to synthesize the law of optimal control, we must use the complete (original) mathematical model of the dynamic system, but to calculate it at one time or another, it is enough reduced model. This consideration defines the principle of informational dualism. An illustrative example is given. It has been shown that this approach can be used to solve some classes of differential games.

Convex Optimization-Based Techniques for Trajectory Design and Control of Nonlinear Systems with Polytopic Range

This paper presents new techniques for the trajectory design and control of nonlinear dynamical systems. The technique uses a convex polytope to bound the range of the nonlinear function and associates with each vertex an auxiliary linear system. Provided controls associated with the linear systems can be generated to satisfy an ordering constraint, the nonlinear control is computable by the interpolation of controls obtained by convex optimization. This theoretical result leads to two numerical approaches for solving the nonlinear constrained problem: one requires solving a single convex optimization problem and the other requires solving a sequence of convex optimization problems. The approaches are applied to two practical problems in aerospace engineering: a constrained relative orbital motion problem and an attitude control problem. The solve times for both problems and approaches are on the order of seconds. It is concluded that these techniques are rigorous and of practical use in solving nonlinear trajectory design and control problems.

Newton-Based Extremum Seeking for Dynamic Systems Using Kalman Filtering: Application to Anaerobic Digestion Process Control

In this paper, a new Newton-based extremum-seeking control for dynamic systems is proposed using Kalman filter for gradient and Hessian estimation as well as a stochastic perturbation signal with time-varying amplitude. The obtained Kalman filter based Newton extremum-seeking control (KFNESC) makes it possible to accelerate the convergence to the extremum and attenuate the steady-state oscillations. The convergence and oscillation attenuation properties of the closed-loop system with KFNESC are considered, and the proposed control is applied to a two-stages anaerobic digestion process in order to maximize the hydrogen production rate, which has better robustness and a slower steady-state oscillation with the comparison of Newton-based ESC and sliding mode ESC.

Structured Learning of Safety Guarantees for the Control of Uncertain Dynamical Systems

Approaches to keeping a dynamical system within state constraints typically rely on a model-based safety condition to limit the control signals. In the face of significant modeling uncertainty, the system can suffer from important performance penalties due to the safety condition becoming overly conservative. Machine learning can be employed to reduce the uncertainty around the system dynamics, and allow for higher performance. In this article, we propose the safe uncertainty-learning principle, and argue that the learning must be properly structured to preserve safety guarantees. For instance, robust safety conditions are necessary, and they must be initialized with conservative uncertainty bounds prior to learning. Also, the uncertainty bounds should only be tightened if the collected data sufficiently captures the future system behavior. To support the principle, two example problems are solved with control barrier functions: a lane-change controller for an autonomous vehicle, and an adaptive cruise controller. This work offers a way to evaluate whether machine learning preserves safety guarantees during the control of uncertain dynamical systems. It also highlights challenging aspects of learning for control.

Robust data-driven control for nonlinear systems using the Koopman operator*

Data-driven analysis and control of dynamical systems have gained a lot of interest in recent years. While the class of linear systems is well studied, theoretical results for nonlinear systems are still rare. In this paper, we present a data-driven controller design method for discrete-time control-affine nonlinear systems. Our approach relies on the Koopman operator, which is a linear but infinite-dimensional operator lifting the nonlinear system to a higher-dimensional space. Particularly, we derive a linear fractional representation of a lifted bilinear system representation based on measured data. Further, we restrict the lifting to finite dimensions, but account for the truncation error using a finite-gain argument. We derive a linear matrix inequality based design procedure to guarantee robust local stability for the resulting bilinear system for all error terms satisfying the finite-gain bound and, thus, also for the underlying nonlinear system. Finally, we apply the developed design method to the nonlinear Van der Pol oscillator.

Follow the Clairvoyant: an Imitation Learning Approach to Optimal Control*

We consider control of dynamical systems through the lens of competitive analysis. Most prior work in this area focuses on minimizing regret, that is, the loss relative to an ideal clairvoyant policy that has noncausal access to past, present, and future disturbances. Motivated by the observation that the optimal cost only provides coarse information about the ideal closed-loop behavior, we instead propose directly minimizing the tracking error relative to the optimal trajectories in hindsight, i.e., imitating the clairvoyant policy. By embracing a system level perspective, we present an efficient optimization-based approach for computing follow-the-clairvoyant (FTC) safe controllers. We prove that these attain minimal regret if no constraints are imposed on the noncausal benchmark. In addition, we present numerical experiments to show that our policy retains the hallmark of competitive algorithms of interpolating between classical H2 and H∞ control laws – while consistently outperforming regret minimization methods in constrained scenarios thanks to the superior ability to chase the clairvoyant.