Guarantees Closed-loop Stability Research Articles

Direct Search Algorithm for Load Frequency Control of a Time-Delayed Electric Vehicle Aggregator

This article addresses the topic of frequency regulation of a single-area power system connected to an electric vehicle (EV) aggregator over a non-ideal communication network. It is considered that the command control action is received by the EV aggregator with constant delay and the power system includes uncertain parameters. Due to the presence of uncertainties and the delay term, the frequency regulation problem is non-convex and hard to solve. The present approaches in the literature convert the non-convex control design problem into a convex problem with a set of Linear Matrix Inequalities (LMIs), which is conservative and in many cases results infeasibility. In this paper, an innovative iterative algorithm, called direct search, is employed for the time-delayed system to design the unknown parameters of a pre-assumed controller. The controller choice is not limited and various controllers’ structures can be assumed. Without loss of generality, a proportional-integral (PI) controller is designed. The novel direct search algorithm can determine a feasible solution whenever at least one solution lays in the design space. Hence, by selecting a wide design space, we can anticipate that the PI controller guarantees closed-loop stability. Numerical simulations are carried out to demonstrate the performance of the developed controller compared to the state-of-the-art approach.

Event-triggered adaptive control of hypersonic vehicles subject to actuator nonlinearities

This paper investigates the event-triggered adaptive control problem for air-breathing hypersonic vehicles (AHVs) subject to physical actuator nonlinearities. In contrast with abundant AHV control strategies belonging to the traditional sample-data framework, the presented adaptive control works with an event-triggered mechanism, which naturally reduces the executing frequency of scramjet fuel-to-air equivalency ratio (FER) and aerodynamic control surface (ACS). During the event-triggered controller design, practical actuator characteristics including magnitude-rate composite constraints and servo transient dynamics are synthetically considered. In the velocity loop, the built-in FER saturation, which is a fusion of physical FER magnitude and rate constraints, is handled by reshaping the velocity reference with the help of an adaptive reference governor. Meanwhile in the altitude loop, a neural control allocator directly generates feasible ACS commands via a neural network that is well trained by means of the optimal control allocation. As the result, ACS magnitude-rate composite constraints and servo transient dynamics can be accommodated without implementing any time-consuming optimization searching process. Theoretical analysis indicates the guaranteed closed-loop stability and tracking performance while excluding the undesired Zeno behavior. Simulations validate the effectiveness of the proposed event-triggered adaptive control.

Transient Performance of MPC for Tracking

We analyse the closed-loop performance of a model predictive control (MPC) for tracking formulation with artificial references. It has been shown that such a scheme guarantees closed-loop stability and recursive feasibility for any externally supplied reference, even if it is unreachable or time-varying. The basic idea is to consider an artificial reference as an additional decision variable and to formulate generalised terminal ingredients with respect to it. In addition, its offset is penalised in the MPC optimisation problem, leading to closed-loop convergence to the best reachable reference. In this paper, we provide a transient performance bound on the closed loop using MPC for tracking. We employ mild assumptions on the offset cost and scale it with the prediction horizon. In this case, an increasing horizon in MPC for tracking recovers the infinite horizon optimal solution.

Passivity-Based Control of Multiple Quadrotors Carrying a Cable-Suspended Payload

In this article, a new passivity-based controller is proposed for stable cotransportation of a cable-suspended payload by a number of quadrotors. Nominal proportional–derivative position controllers with desired acceleration feedforward are augmented with time-varying dissipative terms to account for the drones’ underactuation. A storage function is defined that includes terms inspired by the kinetic and potential energies of the system components as well as virtual energy of the controller. A time-domain passivity observer is used in conjunction with an adaptive dissipative term to ensure that the value of the storage function is continuously decreased and, hence, guarantees closed-loop stability. Moreover, barrier Lyapunov functions are employed to avoid interdrone collisions. The proposed controller makes no assumption about and requires no knowledge of the cables’ tension status. Additionally, it requires no measurement from the payload. The cables can be attached to the quadrotors and the payload at arbitrary points. Experiments with a system of three quadrotors and a cable-suspended payload demonstrate the effectiveness of the proposed approach.

Scaling beyond Bandwidth Limitations: Wireless Control with Stability Guarantees under Overload

An important class of cyber-physical systems relies on multiple agents that jointly perform a task by coordinating their actions over a wireless network. Examples include self-driving cars in intelligent transportation and production robots in smart manufacturing. However, the scalability of existing control-over-wireless solutions is limited as they cannot resolve overload situations in which the communication demand exceeds the available bandwidth. This article presents a novel co-design of distributed control and wireless communication that overcomes this limitation by dynamically allocating the available bandwidth to agents with the greatest need to communicate. Experiments on a real cyber-physical testbed with 20 agents, each consisting of a low-power wireless embedded device and a cart-pole system, demonstrate that our solution achieves significantly better control performance under overload than the state of the art. We further prove that our co-design guarantees closed-loop stability for physical systems with stochastic linear time-invariant dynamics.

Robust output feedback stabilization of an ODE–PDE–ODE interconnection

We propose a controller that robustly stabilizes an interconnection of Ordinary Differential Equations with two hyperbolic linear Partial Differential Equations. The proposed design guarantees closed-loop asymptotic stability as well as robustness to small delays. The result is obtained through a backstepping approach. A boundary observer is also derived, yielding an output feedback controller with several calibration parameters.

Disturbance observer–based super-twisting sliding mode control for formation tracking of multi-agent mobile robots

This paper presents a super-twisting sliding mode control method for the formation maneuvers of multiple robots. In the real world of applications, the robots suffer from many uncertainties and disturbances that trouble the super-twisting sliding mode formation maneuvers very much. Especially, this issue has the adverse effects on the formation performance when the uncertainties and disturbances have an unknown bound. This paper focuses on this issue and utilizes the technique of disturbance observer to meet this challenge. In terms of the leader–follower framework, this paper investigates the integration of the super-twisting sliding mode control method and the disturbance observer technique. This kind of formation design has the guaranteed closed-loop stability in the sense of Lyapunov. Some simulations are implemented through a multi-robot platform. The results demonstrate that the superiority of the formation design regardless of uncertainties and disturbances.

Constant time horizon prediction-based control for linear systems with time-varying input delay

We introduce a constant time horizon prediction-based controller to compensate for a time-varying input delay in a linear control system. We establish that this controller guarantees closed-loop exponential stability, provided that the time-varying delay remains sufficiently close to its average value D0 and its rate of variation sufficiently small. This conclution only has to hold in average, in a mathematical sense that we specify.

Adaptive Dynamic Programming Using Lyapunov Function Constraints

This letter is concerned with a stabilizing adaptive dynamic programming (ADP) approach to approximate solution of a given infinite-horizon optimal control problem. Since the latter problem cannot, in general, be solved exactly, a parametrized function approximator for the infinite-horizon cost function is introduced in ADP (so called “critic”). This critic is used to adapt the parameters of the function approximator. The so called “actor” in turn derives the optimal input of the system. It is a notoriously hard problem to guarantee closed-loop stability of ADP due to the use of approximation structures in the control scheme. Since at least stabilizability is always assumed in the analyzes of ADP, it is justified to invoke a respective Lyapunov function. The proposed ADP scheme explicitly uses the said Lyapunov function to simultaneously optimize the critic and guarantee closed-loop stability. A Hessian-free optimization routine is utilized for the actor and critic optimization problems. Convergence to prescribed vicinities of the optima is shown. A computational study showed significant performance improvement for the critic-based approach compared a nominal stabilizing controller for a range of initial conditions.

Output feedback MPC based on smoothed projected kinky inference

In this study, the authors propose a stabilising data-based model predictive controller for systems subject to constraints in which the prediction model is inferred from experimental data of the plant using a machine learning technique. The inference method is a modification of the kinky inference tailored for model predictive control. In particular, the modified method has a lower computational effort and provides smoother predictions than the original method. The controller formulation considers soft constraints in the outputs, hard constraints in the inputs and guarantees closed-loop robust stability as well as performance by means of the use of different control and prediction horizons and a weighted terminal cost. Under the assumption that the model of the system is Hölder continuous, they prove that the closed-loop system is input-to-state stable with respect to the estimation errors. The results are demonstrated in a case study of a continuously stirred-tank reactor.

Self-Triggered Reduced-Attention Output Feedback Control for Linear Networked Control Systems

A major challenge in networked control systems is to reduce the use of shared communication and control resources without compromising the performance of the closed-loop system. Motivated by this challenge, this paper presents an observer-based controller with irregular sampling that reduces the control attention and guarantees closed-loop stability and global ultimate boundedness of the plant's state vector regardless of bounded input and output disturbances. The feedback control design is based on self-triggered control, whereas the observer is based on the block-form state-space representation of the plant. It is shown via analysis and simulation that the overall control law decreases the number of samples without loosing observability and closed-loop stability, reducing the utilization of communication resources.

Output-Feedback Adaptive Neural Controller for Uncertain Pure-Feedback Nonlinear Systems Using a High-Order Sliding Mode Observer.

A novel adaptive neural output-feedback controller for SISO nonaffine pure-feedback nonlinear systems is proposed. The majority of the previously described adaptive neural controllers for pure-feedback nonlinear systems were based on the dynamic surface control (DSC) or backstepping schemes. This makes the control law as well as the stability analysis highly lengthy and complicated. Moreover, there has been very limited research till date on the output-feedback neural controller for this class of the systems. The proposed controller evades adopting adaptive backstepping or DSC scheme through reformulating the original system into the Brunovsky form, which considerably simplifies the control law. Combining a high-order sliding mode observer and single radial-basis function network with universal approximation property, it is shown that the controller guarantees closed-loop system stability in the Lyapunov sense.

Data-Driven Inversion-Based Control of Nonlinear Systems With Guaranteed Closed-Loop Stability

The data-driven inversion-based control (D $^2$ -IBC) approach is a recently introduced control design method for uncertain nonlinear systems, relying on a two degree-of-freedom architecture, with a nonlinear controller and a linear controller running in parallel. Unlike other approaches for nonlinear control, D $^2$ -IBC does not require an accurate modeling of the plant and is computationally efficient. In this paper, we introduce a finite-gain stability sufficient condition for the closed-loop system and prove that such a condition theoretically holds when a suitable constraint is enforced during the controller design. Finally, we compare the original and the modified methods on a benchmark simulation example, regarding control of the Duffing oscillator.

Sampled-data boundary feedback control of 1-D parabolic PDEs

The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D linear parabolic systems on bounded domains. It is shown that the continuous-time boundary feedback applied in a sample-and-hold fashion guarantees closed-loop exponential stability, provided that the sampling period is sufficiently small. Two different continuous-time feedback designs are considered: the reduced model design and the backstepping design. The obtained results provide stability estimates for weighted 2-norms of the state and robustness with respect to perturbations of the sampling schedule is guaranteed.

Stable assist-as-needed controller design for a planar cable-driven robotic system

Robot-assisted rehabilitation systems have shown promising advantages over traditional therapist-based methods. The type of the controller has an important role in the efficiency of such systems. In this regard, this paper presents a new assist-as-needed (AAN) controller for 4-cable planar robots. The main purpose is to design a bounded-input AAN controller with an adjustable assistance level and a guaranteed closed-loop stability. The proposed controller involves the advantages of both the model-based and non-model-based AAN controllers, and in this way can increase the efficiency of rehabilitation. The controller aims to follow a desired trajectory by allowing an adjustable tracking error, which enables the human subject to freely move the target limb inside this error area. This feature of the controller gives an important advantage over the existing model-based controllers. The controller also compensates for the dynamic modeling uncertainties of the system through an adaptive neural network. The adaptive term includes a forgetting factor to adjust the assistance level of neural network term. The stability of the closed-loop system is analysed, and the uniformly ultimately bounded stability is proven. The effectiveness of the proposed control scheme is validated through simulations conducted for gait rehabilitation.

Sampled-data boundary feedback control of 1-D linear transport PDEs with non-local terms

The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D inhomogeneous, linear, transport partial differential equations on bounded domains with constant velocity and non-local terms. It is shown that the emulation design based on the recently proposed continuous-time, boundary feedback, designed by means of backstepping, guarantees closed-loop exponential stability, provided that the sampling period is sufficiently small. It is also shown that, contrary to the parabolic case, a smaller sampling period implies a faster convergence rate with no upper bound for the achieved convergence rate. The obtained results provide stability estimates for the sup-norm of the state and robustness with respect to perturbations of the sampling schedule is guaranteed.

Enhanced Bounded Integral Control of Input-to-State Stable Nonlinear Systems

Abstract The bounded integral controller (BIC) was recently proposed to replace the traditional integral controller (IC) for the regulation of any input-to-state stable (ISS) nonlinear system and guarantee closed-loop system stability with a bounded control output. In this paper, an enhanced version of the BIC is presented to provide a better approximation of the traditional IC in the entire bounded range of the control output and relax the assumption on the selection of the initial conditions of the original BIC. Using Lyapunov methods, it is analytically proven that the enhanced BIC maintains the zero-gain property and guarantees closed-loop stability of any nonlinear ISS plant with a given bound at the control output, without suffering from integrator windup issues. The plant dynamics and structure can be unkown as long as the plant is ISS. Hence, the proposed enhanced version of the BIC can replace the traditional IC in many applications where closed-loop stability cannot be proven, without changing the controller operation. A practical example is simulated to verify the performance of the proposed enhanced BIC compared to the original version and the traditional IC.

Bounded Integral Control of Input-to-State Practically Stable Nonlinear Systems to Guarantee Closed-Loop Stability

A fundamental problem in control systems theory is that stability is not always guaranteed for a closed-loop system even if the plant is open-loop stable. With the only knowledge of the input-to-state (practical) stability (ISpS) of the plant, in this note, a bounded integral controller (BIC) is proposed which generates a bounded control output independently from the plant parameters and states and guarantees closed-loop system stability in the sense of boundedness. When a given bound is required for the control output, an analytic selection of the BIC parameters is proposed and its performance is investigated using Lyapunov methods, extending the result for locally ISpS plant systems. Additionally, it is shown that the BIC can replace the traditional integral controller (IC) and guarantee asymptotic stability of the desired equilibrium point under certain conditions, with a guaranteed bound for the solution of the closed-loop system. Simulation results of a dc/dc buck-boost power converter system are provided to compare the BIC with the IC operation.

Guaranteeing stable tracking of hybrid position–force trajectories for a robot manipulator interacting with a stiff environment

This work considers the control of a manipulator with the aim of executing desired time-varying motion–force trajectories in the presence of a stiff environment. In several situations, the interaction with the environment constrains just one degree of freedom of the manipulator end-effector. Focusing on this contact degree of freedom, a switching position–force controller is considered to perform the hybrid motion–force tracking task. To guarantee input-to-state stability of the switching closed-loop system, a novel stability result and sufficient conditions are presented. The switching occurs when the manipulator makes or breaks contact with the environment. The analysis shows that to guarantee closed-loop stability while tracking arbitrary time-varying motion–force profiles with a rigid manipulator, the controller should implement a considerable (and often unrealistic) amount of damping, resulting in inferior tracking performance. Therefore, we use the stability analysis technique developed in this paper to analyze a manipulator equipped with a compliant wrist. Guidelines are provided for the design of the wrist compliancy while employing the switching control strategy, such that stable tracking of a motion–force reference trajectory can be achieved and bouncing of the manipulator against the stiff environment can be avoided. Numerical simulations are presented to illustrate the effectiveness of the approach.

Online Learning ARMA Controllers With Guaranteed Closed-Loop Stability.

This paper presents a novel online block adaptive learning algorithm for autoregressive moving average (ARMA) controller design based on the real data measured from the plant. The method employs ARMA input-output models both for the plant and the resulting closed-loop system. In a sliding window, the plant model parameters are identified first offline using a supervised learning algorithm minimizing an ε -insensitive and regularized identification error, which is the window average of the distances between the measured plant output and the model output for the input provided by the controller. The optimal controller parameters are then determined again offline for another sliding window as the solution to a constrained optimization problem, where the cost is the ε -insensitive and regularized output tracking error and the constraints that are linear inequalities of the controller parameters are imposed for ensuring the closed-loop system to be Schur stable. Not only the identification phase but also the controller design phase uses the input-output samples measured from the plant during online learning. In the developed online controller design method, the controller parameters can always be kept in a parameter region providing Schur stability for the closed-loop system. The ε -insensitiveness provides robustness against disturbances, so does the regularization better generalization performance in the identification and the control. The method is tested on benchmark plants, including the inverted pendulum and dc motor models. The method is also tested on an emulated and also a real dc motor by online block adaptive learning ARMA controllers, in particular, Proportional-Integral-Derivative controllers.