Controller Design Problem Research Articles

Decentralized $H_{\infty }$ Control for Switched Interconnected Large-Scale Systems: A Computationally Attractive Method

This article investigates the decentralized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> controller design problems for switched interconnected large-scale systems (ILSSs). The designed decentralized controllers are dependent on the switching modes which can reduce the conservatism. Sufficient conditions are established for ensuring the asymptotic stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance of the studied switched ILSSs. Novel computationally attractive mode-dependent controller deign method is derived. The established controller design conditions eliminate the computationally expensive matrix inversion terms and are given in terms of linear matrix inequalities. Finally, the validness of the proposed decentralized controller design method is verified by the interconnected continuous stirred-tank reactor systems. Other three numerical examples are also performed to show the advantages and superiorities of the derived theoretical results.

New Insights on Robust Control of Tilting Trains with Combined Uncertainty and Performance Constraints

A rigorous study on optimized robust control is presented for non-preview (nulling-type) high-speed tilting rail vehicles. The scheme utilizes sensors on the vehicle’s body, contrary to that of preview tilt (which uses prior rail track information). Tilt with preview is the industrial norm nowadays but is a complex scheme (both in terms of inter-vehicle signal connections and when it comes to straightforward fault detection). Non-preview tilt is simple (as it essentially involves an SISO control structure) and more effective in terms of (the localization of) failure detection. However, the non-preview tilt scheme suffers from performance limitations due to non-minimum-phase zeros in the design model (due to the compound effect of the suspension dynamic interaction and sensor combination used for feedback control) and presents a challenging control design problem. We proposed an optimized robust control design offering a highly improved non-preview tilt performance via a twofold model representation, i.e., (i) using the non-minimum phase design model and (ii) proposing a factorized design model version with the non-minimum phase characteristics treated as uncertainty. The impact of the designed controllers on tilt performance deterministic (curving acceleration response) and stochastic (ride quality) trade-off was methodically investigated. Nonlinear optimization was employed to facilitate fine weight selection given the importance of the ride quality as a bounded constraint in the design process.

Asynchronous secure controller design for singularly perturbation stochastic semi-Markov jump CPSs with the memory-based dynamic event-triggered scheme against complex cyber-attacks

In this paper, the problem of asynchronous secure controller design for singular perturbation stochastic semi-Markov jump systems (SPSS-MJSs) against complicated cyber-attacks is addressed. Firstly, the unified framework for multi-channel spoofing attacks and DoS attacks is properly established for CPSs with the unreliable communication network. Then, by introducing a register, we propose the memory-based dynamic event-triggered scheme (MDETS), which can save resources for the bandwidth limited network to a certain degree. Since the mode information of Markov chain for the secure controller is often unavailable, a hidden Markov model (HMM) is used to formulate the asynchronous situation between the mode of original system and the constructed controller. Further, by constructing Lyapunov functionals and utilizing linear matrix inequality (LMI) techniques, the obtained closed-loop SPSS-MJSs are endowed with an exponential stability criterion. And the co-design of the asynchronous secure controller and MDETS is presented. Finally, a practical example of the specific small capacitance circuit system is offered to verify the feasibility and superiority of the developed method.

Deep Reinforcement Learning Control of Fully-Constrained Cable-Driven Parallel Robots

Cable-driven parallel robots (CDPRs) have complex cable dynamics and working environment uncertainties, which bring challenges to the precise control of CDPRs. This paper introduces the reinforcement learning to offset the negative effect on control performance of CDPRs resulting from the uncertainties. The problem of controller design for CDPRs in the framework of deep reinforcement learning is investigated. A learning based control algorithm is proposed to compensate for uncertainties due to cable elasticity, mechanical friction, etc. A basic control law is given for the nominal model, and a Lyapunov-based deep reinforcement learning control law is designed. Moreover, the stability of the closed-loop tracking system under the reinforcement learning algorithm is proved. Both simulation and experiments validate the effectiveness and advantages of the proposed control algorithm.

3D trajectory tracking of underactuated non-minimum phase underwater vehicles

This paper studies the 3D trajectory tracking problem for a class of torpedo-type underwater vehicles which are a typical underactuated and also non-minimum phase systems. Two spherical coordinate transformations are introduced to transform the vehicles’ tracking model into a certain three-input-three-output form which, unfortunately, is not in a strict-feedback form. To avoid possible singularity problem in the recursive control design, an exponential modification of orientation (EMO) concept is introduced and forces the vehicles to track this modified trajectory instead of directly tracking the reference one. As for the non-minimum phase problem, since the input matrix in the transformed three-input-three-output form is always invertible, this problem can be easily handled in this paper. Numerical studies are also carried out to verify the effectiveness of the proposed tracking scheme.

Observer-Based Control of Inductive Wireless Power Transfer System Using Genetic Algorithm

In this paper, we studied the feedback stabilization of an inductive power transfer system based on available output measurement. The proposed controller relies on a full-order state observer in order to estimate the unmeasured state. The control design problem is challenging due to the large dimension of the closed-loop system, which requires too many tuning parameters to be determined when conventional control methods are employed. To solve this issue, we propose an LQR methodology based on a genetic algorithm such that the weighing coefficients of the cost function matrices can be automatically computed in an optimized manner. The proposed approach combines the method of eigenstructure assignment and the LQR technique in order to design both the controller and the observer gain matrices. The design methodology provides a systematic way to compute the parameters of the LQR technique for a wireless power transfer system in an optimized manner, which can be a useful design tool for many other applications. The effectiveness of the approach was verified by numerical simulation on the dynamic model of the wireless power transfer system. The results show that the proposed design outperforms conventional design methods in terms of a better performance and reduced design iterations effort.

Improved Dynamic Event-Triggered Robust Control for Flexible Robotic Arm Systems with Semi-Markov Jump Process

In this paper, we investigate the problem of a dynamic event-triggered robust controller design for flexible robotic arm systems with continuous-time phase-type semi-Markov jump process. In particular, the change in moment of inertia is first considered in the flexible robotic arm system, which is necessary for ensuring the security and stability control of special robots employed under special circumstances, such as surgical robots and assisted-living robots which have strict lightweight requirements. To handle this problem, a semi-Markov chain is conducted to model this process. Furthermore, the dynamic event-triggered scheme is used to solve the problem of limited bandwidth in the network transmission environment, while considering the impact of DoS attacks. With regard to the challenging circumstances and negative elements previously mentioned, the adequate criteria for the existence of the resilient H∞ controller are obtained using the Lyapunov function approach, and the controller gains, Lyapunov parameters and event-triggered parameters are co-designed. Finally, the effectiveness of the designed controller is demonstrated via numerical simulation using the LMI toolbox in MATLAB.

Robust Adaptive Composite Learning Integrated Guidance and Control for Skid-to-Turn Interceptors Subjected to Multiple Uncertainties and Constraints

This paper investigates a novel robust adaptive dynamic surface control scheme based on the barrier Lyapunov function (BLF), online composite learning, disturbance observer, and improved saturation function. It is mainly designed for a class of skid-to-turn (STT) interceptor integrated guidance and control (IGC) design problems under multi-source uncertainties, state constraints, and input saturation. The serial-parallel estimation model used in this study estimates the system states and provides “critic” information for the neural network and disturbance observer; then, these three are combined to realize online composite learning of the multiple uncertainties of the system and improve the interception accuracy. In addition, the state and input constraints are resolved by adopting the BLF and the improved saturation function, while the design of the auxiliary system ensures stability. Finally, a series of simulation results show that the proposed IGC scheme with a direct-hit intercept strategy achieves a satisfactory effect, demonstrating the validity and robustness of the scheme.

The observed mode dependent controller design problem for a class of continuous‐time hidden semi‐Markov jump systems

SummaryThis paper studies the stability analysis and stabilization synthesis problems for a class of continuous‐time jump systems with hidden system modes. To precisely model the switching signals of the considered systems, a novel definition of continuous‐time hidden semi‐Markov process is proposed based on the notions of emission probability and time varying dual‐index transition rate. By virtue of such definition, a dual‐index Lyapunov function is utilized to derive the sufficient stability conditions of the considered systems. By adopting a technology that can decouple the nonlinear terms in the above conditions, the numerically testable existence conditions of the controller for the resulting stabilizing systems are presented. An example is given to illustrate the effectiveness of our results.

Model-Reference Adaptive Control of Finite State Machines With Respect to States: A Matrix-Based Approach

To control a system with model uncertainty, adaptive control is an available approach. In this paper we investigate adaptive control in the field of finite state machines with respect to states. The task of the adaptive control is to synthesize an unfixed-parameter controller that invokes an adaptive law to realize a desired behavior. Especially, the adaptive law relies on a reference model. Thus, the title of model-reference adaptive control is adopted. We derive a sufficient and necessary condition for the existence of such an adaptive controller. Based on the condition, the corresponding controller design problem is resolved. As the design process, semi-tensor product of matrices is the core mathematical tool. Thus, for finite state machines with respect to states, model-reference adaptive control is incorporated into the framework of semi-tensor product of matrices.

Extension of iterative learning control design for batch processes with time-delay in the input subject to random cycle-varying uncertainties

For uncertain time-delay batch processes with repetitive nature, this work deals with an unresolved problem of robust iterative learning control (ILC) design, in which we simultaneously remove the conventional assumptions of cycle-invariant uncertainties in reference trajectories, initial states, external disturbances, process dynamics, and time-delay. Moreover, we consider the variation of all existing uncertainties from a random point of view. Based on the idea of the internal model control (IMC) and indirect ILC, a novel IMC-based ILC structure is proposed. Then, we derive the practical convergence conditions, which have two design functions. By introducing a simple method for adjusting these functions, not only can we ensure that the expected tracking error converges monotonically to zero-neighborhood (in the L2-norm sense) but we can also achieve an acceptable convergence rate. Moreover, it is shown that the satisfaction of derived convergence conditions can always be guaranteed for any process. Simulation tests are provided to demonstrate the effectiveness of the proposed design.

Convex Approach to Data-Driven Off-Road Navigation via Linear Transfer Operators

We consider the problem of optimal control design for navigation on off-road terrain. We use a traversability measure to characterize the difficulty of navigation on off-road terrain. The traversability measure captures terrain properties essential for navigation, such as elevation maps, roughness, slope, and texture. The terrain with the presence or absence of obstacles becomes a particular case of the proposed traversability measure. We provide a convex formulation to the off-road navigation problem by lifting the problem to the density space using the linear Perron-Frobenius (P-F) operator. The convex formulation leads to an infinite-dimensional optimal navigation problem for control synthesis. We construct the finite-dimensional approximation of the optimization problem using data. We use a computational framework based on the data-driven approximation of the Koopman operator. This makes the proposed approach data-driven and applicable to cases where an explicit system model is unavailable. Finally, we apply the proposed navigation framework with single integrator dynamics and Dubin's car model.

Observer-Based Output-Feedback Control for Nonlinear Time-Delay Systems

In this article, the output feedback control design problem for a class of strict-feedback nonlinear systems with unknown state time-varying delays is addressed. Two output feedback control schemes are considered which are based on full-order and reduced-order observer, respectively. Lyapunov–Krasovskii functionals with static gain are used to develop novel memoryless control strategies. The above work ensures that all the signals in the closed-loop system are bounded and the system is asymptotically stable. Finally, two simulation examples illustrate the effectiveness of the two control schemes we proposed.

Antidisturbance Control Design for Interval Type-2 Fuzzy Stochastic Systems With Input Quantization

Quantized anti-disturbance control design problem is presented for a class of interval type-2 (IT2) fuzzy stochastic systems subject to time delays and multiple disturbances. The inherent uncertain nonlinear and hybrid characteristics of the concerned system make it difficult to design a stable anti-disturbance controller. In order to properly reflect the characteristics of IT2 fuzzy stochastic models with multiple disturbances, a new fuzzy disturbance observer is proposed to estimate the disturbances generated by a fuzzy exogenous system. Furthermore, a quantized fuzzy anti-disturbance control scheme is synthesized by fusing the estimation of the multiple disturbances. With the support of Lyapunov functional method, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$It{\hat{o}}$</tex-math></inline-formula> 's formula and auxiliary function-based integral inequality, the resulting IT2 fuzzy stochastic systems are proved to be robustly stochastically stable with mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> /passivity performance index. The design methods of the fuzzy disturbance observer and quantized anti-disturbance controller are formulated in the form of linear matrix inequalities so that the corresponding gain matrices can be easily obtained. Finally, simulation studies on three examples are provided to justify the efficiency of the designed control strategy.

Leveraging Morphological Computation for Controlling Soft Robots: Learning from Nature to Control Soft Robots

Traditional robot designs typically employ rigid body parts and high-torque servo motors. This helps to obtain simple reproducible models and, therefore, to facilitate control. Soft robotics is a new research field that deliberately expands the design toolbox to a wide range of smart and, often, soft materials. This approach is generally inspired by the remarkable performance of biological systems, which use soft structures to interact successfully with noisy and hard-to-model environments and, as a result, outperform state-of-the-art robots in open-world scenarios. However, using soft bodies comes with a significant disadvantage. Soft materials often have complex and nonlinear dynamics, which makes them hard to model and therefore difficult to control. To fulfill the potential of soft robotics to achieve performances close to biological systems, this control problem has to be solved. A promising solution is another bioinspired principle called morphological computation, which proposes to outsource functionality directly to the body morphology. From this point of view, the seemingly undesired nonlinear dynamics become a resource for implementing nonlinear functionalities. This extends the control design problem to the question of how to design the body morphology of the robot. While there exist proofs of concept that demonstrate the potential of this approach, the existing work (for the most part) is lacking mathematical rigor and a general framework. We believe that the control community has the right set of tools to support the development of a design framework for morphological computation. The goal of this article (see “Summary”) is to provide an introduction to the concepts of soft robotics and morphological computation, explain how they can work together, and (with the help of examples) illustrate their potential for control. The hope is to inspire members of the control community to develop novel control frameworks for the next generation of soft robots.

Current sharing and voltage regulation of parallel DC–DC buck converters: Switching control approach

In this paper, a new framework for distributed switching control of parallel DC–DC buck converters is investigated, which represents voltage regulation and current sharing as two decoupled control design problems. The problem is described as a cascaded switched affine system with the new variables output voltage, total current, and current difference of the load, and by employing distributed min-projection switching technique, switching control signals are provided to achieve both voltage regulation and current sharing control objectives. Stability analysis based on relay control is carried out to guarantee the asymptotic stability of the error signals. Finally, the performance and effectiveness of the proposed control strategy are demonstrated by simulation studies as well as experiments conducted on a laboratory prototype.

Kernel-based regularized iterative learning control of repetitive linear time-varying systems

For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is not chosen carefully, models with either large variance or large bias would be resulted, which is one of the obstacles to further improve the modeling and tracking performances of data-driven ILC in practice. An emerging trend in the system identification community to deal with this issue is using regularization instead of the statistical tests, e.g., AIC, BIC, and one of the representatives is the so-called kernel-based regularization method (KRM). In this paper, we integrate KRM into data-driven ILC to handle a class of repetitive linear time-varying systems, and moreover, we show that the proposed method has ultimately bounded tracking error in the iteration domain. The numerical simulation results show that in contrast with the least squares method and some existing data-driven ILC methods, the proposed one can give faster convergence speed, better accuracy and robustness in terms of the tracking performance.

Boundary Vibration Constraint Control Design of Motor-Driven Industrial Moving Belt Systems Subject to Actuator Input Saturation

This paper investigates the adaptive controller design problem for a class of motor-driven industrial belt systems with boundary vibration constraints and actuator input saturation. The operating equations of the considered system are obtained based on the Eulerian description and Hamilton’s principle, and an auxiliary system is desiigned to compensate for the input saturation effect of the actuator. In a practical engineering context, the system is not only affected by the time-varying boundary disturbances but also the key parameters of the whole closed-loop system are unknown. For this reason, a disturbance observer and the adaptive laws are designed to estimate the disturbances suffered by the system and to compensate for the parameter uncertainty of the system, respectively. With the application of our designed control strategy, the boundary vibration of the system are shown to satisfy the constraint, i.e., the safe operation of the motor-driven industrial belt system is ensured. Finally, the stability and effectiveness of the designed control scheme are demonstrated by examples of numerical simulations.

Reduced-Order Static -Gain Control of Rotorcraft with Guaranteed Rotor–Fuselage Stability

A reduced-order control design method for rotorcraft is proposed in this work. Explicit constraints on the closed-loop fuselage–rotor stability are considered in the fuselage dynamics-based control design, aiming for the -gain performance for the fuselage dynamics under pole placement constraints and the guaranteed fuselage–rotor stability. Sufficient conditions for the control design problem are presented, formulated as a feasibility problem based on bilinear matrix inequalities. Such an NP-hard problem is approximated using convex relaxation techniques and the cone complementary linearization method, leading to an iterative control design algorithm. An altitude–velocity vector tracking concept is also proposed in this work, integrated with the proposed control design method to design rotorcraft trajectory controllers. Performance of the resultant rotorcraft trajectory controllers is examined via numerical simulations against representative maneuvers from the ADS-33E specification.

Adaptive control for multi-agent systems with actuator fault via reinforcement learning and its application on multi-unmanned surface vehicle

In this paper, the adaptive cooperative control problem is studied for a class of second order multi-agent systems (MASs) with actuator fault via reinforcement learning (RL). The strategic utility function is approximated by the critic neural network (NN), and the uncertain dynamics in MASs are estimated by the action NN. The NN weight vectors are updated by employing the gradient descent strategy. Then, the distributed RL control strategy is developed to solve the consensus control design problem. In comparison with the existent RL control results, the actuator fault is taken into consideration in the controller design. The stability analysis is given based on the Lyapunov theory, and all signals in the closed-loop system are guaranteed to semi-globally uniformly ultimately bounded (SGUUB). Two simulation examples, including a multi-unmanned surface vehicle system, are presented to demonstrate the validation of this strategy.