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This study investigates the problem of fault estimation and control for unknown discrete-time systems. Such a problem was first formulated as an multiobjective optimization problem. Then, a data-driven parameterization controller design method was proposed to optimize both fault estimation and robust control performances. In terms of the single-objection control problem, necessary and sufficient conditions for designing the suboptimal controller were presented, and the performance index optimized by the developed data-driven method was shown to be consistent with that of the model-based method. In addition, by introducing additional slack variables into the controller design conditions, the conservatism of solving the multiobjective optimization problem was reduced. Furthermore, contrary to the existing data-driven controller design methods, the initial stable controller was not required, and the controller gain was directly parameterized by the collected state and input data in this work. Finally, the effectiveness and advantages of the proposed method are shown in the simulation results.

Microgrid is a key to an efficient and resilient power grid operation. Thus in this paper, a robust control scheme is implemented namely modified frequency locked loop (MFLL), proficient in eliminating the voltage and current fluctuations because of phase/frequency variation. Therefore, enhancing the consistency of the supply across nonlinear load through a smooth transition from utility-interactive to islanded mode. It also achieves accelerated convergence and reduced steady-state error. MFLL is an easy control technique, with only one interfacing voltage source converter, which delivers a stable supply to critical loads during different operating modes. The implemented system has the main advantage of the capability of power-sharing between distributed generations (DGs) systems while regulating the voltage at the DC link. It also provides power quality improvement through harmonics suppression; voltage regulation during contingencies like unbalance in load and compensation in reactive power at the common coupling point following the prerequisite of the system. The performance through the implemented control algorithm is brought about in MATLAB 15b/Simulink platform. The performances of results are compared with already reported control strategies. Thus, simulated results comparison with existing work presents the competence of the implemented control strategy under dynamic conditions.

Automated vehicles require efficient and safe planning to maneuver in uncertain environments. Largely this uncertainty is caused by other traffic participants, e.g., surrounding vehicles. Future motion of surrounding vehicles is often difficult to predict. Whereas robust control approaches achieve safe, yet conservative motion planning for automated vehicles, Stochastic Model Predictive Control (SMPC) provides efficient planning in the presence of uncertainty. Probabilistic constraints are applied to ensure that the maximal risk remains below a predefined level. However, safety cannot be ensured as probabilistic constraints may be violated, which is not acceptable for automated vehicles. Here, we propose an efficient trajectory planning framework with safety guarantees for automated vehicles. SMPC is applied to obtain efficient vehicle trajectories for a finite horizon. Based on the first optimized SMPC input, a guaranteed safe backup trajectory is planned using reachable sets. This backup is used to overwrite the SMPC input if necessary for safety. Recursive feasibility of the safe SMPC algorithm is proved. Highway simulations show the effectiveness of the proposed method regarding performance and safety.

The control of a microgrid is quite challenging thus this work implements a robust and fast control technique based on circular limited cycle oscillator frequency locked loop with inner loop filter (CLO-FLL-WIF) for switching operation between an islanded and the grid-connected modes. This microgrid combing solar PV (Photovoltaic) generation, SyRG (Synchronous Reluctance Generator) for pico-hydro generation, and the battery, which works in both standalone and grid-connected modes while feeding local loads uninterruptedly. The output power conversion of a PV array is influenced by irradiation of solar PV array and has low efficiency, therefore, a MPPT (Maximum Power Point Tracking) namely an INC (Incremental Conductance) method is used. In the implemented system, the interfaced power converter is gated in the grid-connected mode and islanded mode using same enhanced second order generalized integrator with a modified frequency locked loop (ESOGI-MFLL) control method. The comparative results validate that the response of ESOGI-MFLL in comparison to the existing control algorithm, is faster under load and generation perturbations. The implemented control techniques are used for fundamental extraction of load component of voltage and current for assessment of reference currents with their respective phases of synchronization while maintaining the required IEEE power quality standard-519. Simulated results of a microgrid for grid-tied PV-BES-SyRG are obtained in MATLAB/Simulink platform to demonstrate its performance.

In this article, the problem of H∞ codesign for nonlinear control systems with unmatched uncertainties and adjustable parameters is investigated. The main purpose is to solve the adjustable parameters and H∞ controller simultaneously so that better robust control performance can be achieved. By introducing a bounded function and defining a special cost function, the problem of solving the Hamilton-Jacobi-Isaacs equation is transformed into an optimization problem with nonlinear inequality constraints. Based on the sum of squares technique, a novel policy iteration algorithm is proposed to solve the problem of the H∞ codesign. Moreover, one modified algorithm for optimizing the robust performance index is given. The convergence and the performance improvement of new iteration policy algorithms are proved. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms.

Navigation control of microrobots in vivo has great potential in precision medicine and has attracted considerable attention in recent years. The control performance of the existing methods is considerably affected by hysteresis nonlinearity. This article presents a robust control method that can overcome hysteresis influence in navigating a microrobot actuated by an electromagnetic coil system. A motion planner that combines the breadth-first search (BFS) method and genetic algorithm (GA) is used to plan a reliable and flexible trajectory for the microrobot navigation. To compensate for hysteresis nonlinearity existing in the system, the Prandtl-Ishlinskii (PI) model is introduced. A robust controller that integrates adaptive sliding mode control (ASMC) and nonlinear disturbance observer is designed to guarantee the stability and accuracy of the microrobot in motion. Experiments have been performed to demonstrate the effectiveness of the proposed approach. The success of this research will advance the microrobot navigation for in vivo applications.

In robust control under state constraints the set of admissible inputs is usually considered as given, under the assumption that the actuators have been already designed. However, if the input set is too small any controller will fail in stabilizing the closed-loop system while satisfying all prescribed constraints for some initial states of interest, or vice versa the chosen actuators may be over-sized. To handle this issue, in this paper we address the problem of computing the smallest input constraint set such that the closed-loop system is stabilizable from a prescribed set of initial states while respecting all constraints. We focus our attention on linear systems with additive disturbances, and develop the algorithm based on recursive feasibility of robust model predictive control. We demonstrate the results using numerical examples, in which we consider different metrics for the input constraint set selection.

With the objective to eliminate the input current sensor in a totem-pole boost power factor corrector (TPFC) for its low-cost design, a novel discretized sampling-based robust control scheme is proposed in this work. The proposed control methodology proves to be beneficial due to its ease of implementation and its ability to support high frequency operation, while being able to eliminate one sensor, and thus enhancing reliability and cost-effectiveness. In addition to that, detailed closed loop stability analysis is carried out for the controller in discrete domain to ascertain brisk dynamic operation when subjected to sudden load fluctuations. To establish the robustness of the proposed control scheme, a detailed sensitivity analysis of the closed loop performance metrics with respect to undesired changes and inherent uncertainty in system parameters is presented in this paper. A comparison with the state-of-the-art (SOA) methods is provided, and conclusive results in terms of better dynamic performance are also established. To verify and elaborate on the specifics of the proposed scheme, a detailed simulation study is conducted, and the results show 25% reduction in response time as compared to SOA approaches. A 500W boost PFC prototype is developed and tested with the proposed control scheme to evaluate the steady state and dynamic performance.

Due to the simultaneous existence of model uncertainties and external disturbances, designing automated ground vehicle path-following controllers is recognized as a challenging task. The $H_{∞}$ robust control methodology, as one of the accomplished strategies for controller robustification, has been commonly adopted by researchers to address the vehicle path-tracking problems. Nevertheless, despite its advantages, the $H_{∞}$ controller is only capable of limiting the total ``energy'' of the tracking errors. On the other hand, from a safety standpoint, constraining the ``peak'' of the tracking errors may carry an equal or more importance. To establish a guaranteed upper bound on the path-tracking errors, this paper proposes a novel methodology to synthesis the ground vehicle path-following controller in light of the energy-to-peak robust control theory. Additionally, to address the time-varying uncertainties presented in the tire dynamics, robust stabilization constraints based upon the small-gain theorem are also formulated into the overall controller design problem. Comparative study regarding the disturbance rejection performance between the proposed controller and the conventional $H_{∞}$ approach is conducted via CarSim-Simulink joint simulations. Furthermore, the robustness and disturbance attenuation ability of the energy-to-peak path-tracking controller is experimentally verified on a scaled car.

This paper proposes a novel Stackelberg game-oriented optimal control approach to address the bounded constraint-following control problem for uncertain mechanical systems. First, the uncertainties (possibly fast time-varying) in the system are assumed to be bounded with an unknown boundary which lies in a specified fuzzy evidence number. In practical engineering, bounded system performance is always demanded, such as the inequality constraint. A diffeomorphism transformation approach is proposed to transform the constrained system into a restructured one satisfying the bounded constraint. Second, we propose an adaptive robust control oriented by the constraint-following control to render the restructured system to follow the specified constraints accurately with deterministic performance (guaranteeing uniform boundedness and uniform ultimate boundedness). The self-adjusting adaptive law (leakage-type) can compensate for the uncertainties and avoid overcompensation. Third, a Stackelberg game-oriented optimization approach is proposed to obtain the optimal control parameters based on the fuzzy evidence theory. In the optimization approach, the two control parameters, are considered as two players with respective cost functions related to system performance and control cost. Furthermore, the optimization problem is solved by obtaining the Stackelberg strategy, which is proved to exist in analytic form. Ultimately, the permanent magnet synchronous linear motor system simulation is presented to show the design process and the excellent performance of the proposed optimal control scheme.

In this paper, a robust control strategy with a cascade structure is designed for the underactuated unmanned aerial manipulator (UAM) to perform favorable trajectory tracking, in the presence of model uncertainties and time-varying external disturbances (e.g. wind drag). In the position loop, a geometric distance is adopted as the criterion for the thrust design. Besides, both the model uncertainties and external disturbances are compensated by employing a robust term. In the attitude loop, the prescribed performance guarantees are enforced in the controller design to standardize transient performance on attitude errors. In particular, just relying on the necessary feedback states, an auxiliary system, the adaptive control technique, and the disturbance observer are respectively designed to estimate the model uncertainties and external disturbances. Through the Lyapunov stability theory analysis, the proposed approach based on a geometric distance can effectively track the desired trajectory. The results of the comparative simulations study demonstrate the effectiveness and advantages of the proposed approach.

This article is dealt with the problem of trajectory tracking with prescribed performance for a family of underactuated surface vessels (USVs) under model uncertainties and disturbances. The prescribed performance means that the USV tracks a given trajectory with the arbitrarily predefined speed of response and accuracy. The existing prescribed performance control (PPC) solutions and the traditional robust control approaches for USVs may have the singularity issue or cause a discontinuous control signal. Thereby, a new-type adaptive PPC strategy is put forward in this article. The adaptive technique is devoted to tackling model imperfections as usual, whereas the constraint-handling technique is adopted in a novel way. Herein, we first construct an auxiliary variable instead of using the approach angle or azimuth angle. Then, we impose constraints on the position error, not the tracking error, and the auxiliary variable, simultaneously. In this way, the predefined performance is achieved by moreover a singularity-free continuous control action. These theoretical findings are illustrated via a comparative simulation study.

Affine nonlinear systems are special kinds of non-linear systems, and they can represent many practical systems. Dealing with affine nonlinear system based on T-S fuzzy model has drawn much attention in literature recently. In this paper, a robust control method is proposed for affine nonlinear system with disturbance based on T-S fuzzy model. First, an optimization T-S fuzzy model is constructed focusing on optimizing the parameters of the weight functions by using differential evolution algorithm (DEA). Second, in order to reconstruct the disturbance, an interval observer is designed for the affine nonlinear system, and then a novelty disturbance reconstruction method based on the interval observer is developed. The disturbance reconstruction value can asymptotically approach the actual disturbance value, and furthermore, it decouples the control input. Third, by taking the optimization T-S fuzzy model as design model and by introducing the reconstruction of disturbance into controller, a feedback robust controller with disturbance compensation is designed to stabilize the affine nonlinear system. Finally, a simulation example of the crane model is given and some comparisons are provided to verify the effectiveness and show the advantages of the proposed method.

Weight-on-Bit is of vital importance to the drilling trajectory orientation in directional drilling. This paper concerns robust control of drilling trajectory with weight-on-bit uncertainty for the directional drilling process. The objective is to develop an equivalent-input-disturbance-based trajectory control scheme such that the drilling trajectory is precisely controlled by suppressing the fluctuations of weight-on-bit. The motion orientation of both the drill bit and a series of stabilizers is used to describe the evolution process of the drilling trajectory. A state-space model with weight-on-bit uncertainty is derived from the evolution equation through a variable transformation. An equivalent-input-disturbance-based trajectory control system is designed, and two control loops are to track and control the trajectory inclination and azimuth, respectively. Two internal models track the trajectory inclination and azimuth respectively to elevate the control accuracy in the trajectory system. Two observer models combined with two low-pass filters estimate the trajectory inclination and azimuth by measuring the bottom hole assembly’s inclination and azimuth. Some sufficient conditions are derived using linear-matrix-inequalities to obtain the control parameters by considering a reasonable fluctuation range of weight-on-bit. Finally, the control effects in the build-up and horizontal section of the drilling trajectory illustrate the proposed approach’s validity.

This article provides a solution to tube-based output feedback robust model predictive control (RMPC) for discrete-time linear parameter varying (LPV) systems with bounded disturbances and noises. The proposed approach synthesizes an offline optimization problem to design a look-up table and an online tube-based output feedback RMPC with tightened constraints and scaled terminal constraint sets. In the offline optimization problem, a sequence of nested robust positively invariant (RPI) sets and robust control invariant (RCI) sets, respectively, for estimation errors and control errors is optimized and stored in the look-up table. In the online optimization problem, real-time control parameters are searched based on the bounds of time-varying estimation error sets. Considering the characteristics of the uncertain scheduling parameter in LPV systems, the online tube-based output feedback RMPC scheme adopts one-step nominal system prediction with scaled terminal constraint sets. The formulated simple and efficient online optimization problem with fewer decision variables and constraints has a lower online computational burden. Recursive feasibility of the optimization problem and robust stability of the controlled LPV system are guaranteed by ensuring that the nominal system converges to the terminal constraint set, and uncertain state trajectories are constrained within robust tubes with the center of the nominal system. A numerical example is given to verify the approach.

This paper puts forward an unprecedented avoidance-striking-arrival problem aiming to address the need for tank's uncertain mechanical systems on the intelligent battlefield. The associated system uncertainties (possibly rapid) are time-varying but bounded (possibly unknown). The goal is to design a controller that enables the tank to aim at and attack the enemy tank while keeping itself (out of the enemy fire zone). The tank maintains this condition until reaching the predefined region. In this paper, an approximate constraint following control method is adopted to solve this problem, and the original constraints are creatively divided into two categories: the avoidance - tracking constraint and the striking - arrival constraint. An adaptive robust control method is proposed and consequently verified through simulation experiments. It is proved that the system fully obeys the avoidance - tracking - constraint and strictly obeys the striking - arrival constraint under the control input τ . Besides, the control of the tank vehicle running system and tank gun bidirectional stabilization system are unified to deal with the control signal delay caused by complex uncertainties on the battlefield. Overall, this paper reduced the delay of signal transmission in the system while solved the avoidance - striking - arrival problem.

This paper presents a robust path tracking control method by utilizing the ideology of constraint-following approach for uncertain underactuated autonomous vehicles. The uncertainties are bounded with an unknown boundary. They do not all fall within the range space of the input matrix. Based on kinematic relations between the desired path and vehicle, the path tracking task is transformed into an equality constraint of the vehicle lateral dynamics states. The control goal is to make the underactuated vehicle follow the constraint, thus realizing the desired tracking performance. The constraint-following robust control (CFRC) is designed in two steps. First, a servo control design for the nominal system is devised without considering uncertainty and initial constraint deviation. Second, the uncertainty is meticulously decomposed into matched and mismatched portions based on the geometric structural characteristics of the constraint dynamics system. As a result, since the mismatched uncertainty is orthogonal to the constraint-following geometric space, it ``disappears'' in the stability analysis. The matched uncertainty is estimated by a self-adjusting leakage type adaptive law. On this basis, a robust control is designed based on the estimated matched uncertainty. Through Lyapunov minimax analysis, the proposed control method guarantees the approximate constraint-following performance. Finally, the TruckSim-Simulink co-simulations and real vehicle experiments are presented. The results show that the proposed control can robustly realize excellent tracking performance in the presence of time-vary uncertainties.

As one of the core components of high-end manufacturing equipment, linear motor (LM) plays an important role in high efficiency and high quality production of the equipment. In this paper, a high-precision robust control method with periodic dynamic compensation is proposed for the most common repetitive trajectory tracking task in the manufacturing industry. To overcome the influence of unknown periodic dynamics on the control accuracy, a B-spline wavelet neural network (BSWNN) observer is designed to estimate the uncertainties. Moreover, the control framework in the form of robust control is employed to ensure the stability of the closed-loop system under other unknown aperiodic disturbance. Finally, the high-precision control for LM-driven stage in high-speed environment is realized, and the comparative experiments show that the control accuracy of the proposed method is significantly improved at least 28.9% compared with the other three existing control methods.

This study has the aim of introducing a new type of trajectory tracking robust controllers for a class of rehabilitation robotic system considering the articulations restrictions. The robotic device consists of a suspended biped configuration. The suggested robust control considers the application of state depending gains which provide finite-time convergence for the tracking deviation. The state restrictions are fulfilled by the implementation of controller gains estimated by a class of the controlled tangent barrier Lyapunov function. Stability analysis for the tracking error yields the explicit design of the state dependent gains. The rate of convergence for the controller design is enhanced using a matrix inequality convex optimization method. Based on the forward complete characteristic of the suggested rehabilitation device, it is allowed using a finite-time convergent super-twisting-based differentiator to concrete an output feedback realization of the proposed controller. A computerized model of the tendered rehabilitation robot provides a reliable testing platform to the suggested roust controller. Numerical evaluations appear to serve as an indirect confirmation for the tracking error convergence, satisfying the articulation restrictions, and the effect of the gain optimization design. For comparison purposes, the regular state feedback control design is considered as benchmark. The faster convergence of the mean square estimation of the tracking error justifies the design of the proposed control design as well as the state feedback structure justifies the origin is a fixed-time stable equilibrium point for the space of tracking error at the same time that state space restrictions remain satisfied. The experimental evaluations of the proposed controller justifies the barrier controller which, in spite of the modeling uncertainties and the implementation issues, tracked the reference trajectories.

The output-based event-triggered cooperative output regulation problem is addressed for constrained linear heterogeneous multiagent system in this article. In light of the robust control theory, H∞ leader-following consensus with respect to exogenous signals, including both disturbance to be rejected and reference state of leader to be tracked, is guaranteed. Meanwhile, the system performance alleviates degradation through a model recovery anti-windup technique while encountering input saturation. Furthermore, the follower's self-state observer, the leader-state observer, and the anti-windup auxiliary system are integrated into a comprehensive system, and a unified event-triggering mechanism of full states is addressed. A fixed lower bound of sampled interval is adopted such that the frequency of data transmission gets reduced and no Zeno-behavior happens. Both the input and output of the follower's controller and anti-windup compensator hold constant, respectively, during the event-triggered intervals such that the resulting output-based event-triggered controller can be directly implemented in a digital platform. Finally, a simulation example is provided to illustrate the effectiveness.

There is uncertainty in the system, and we consider that uncertainty is (possibly fast) time varying, but with definite bound. Fuzzy set theory is used to describe the inexact boundary and then the problem of robust control of uncertain dynamical systems is studied. Based on two adjustable design parameters, a robust control method for general mechanical systems is proposed. The control is deterministic, not the conventional IF-THEN rule based. By using the Lyapunov minimax approach, it is proved that the proposed control can guarantee system performance to be uniformly bounded and uniformly ultimately bounded. In order to find the optimal solution in the prescribed range, a two-player cooperative game is used. To reduce costs while ensuring control performance, two performance indices are developed, each of which is controlled by an adjustable parameter (i.e., player). Both necessary and sufficient conditions for Pareto-optimality are established. Using these conditions, the Pareto-optimal solution can be obtained. The effectiveness of the control design is demonstrated by the simulation of the two-body pendulum.

The effects of model parameter uncertainty on traffic flow control problems have recently drawn research attention. While the uncertainty in fundamental diagram related parameters has been investigated in the past, few articles have focused on network parameters uncertainty, including turning ratio uncertainty. To fill this gap, this article proposes a robust control model to deal with the uncertainties in the turning ratio by using distributionally robust chance constraints. The model allows one to compute the optimal control action that maximizes some objective, under all possible distributions of network parameters. We then apply this robust control framework to both a freeway network and an urban network, and evaluate the impact of uncertainty on optimal control inputs, over the test networks. The case studies show that compared to non-robust control, the proposed robust model can reduce congestion brought by the uncertainties and improve the overall throughput., Accepted for publication on IEEE Transactions on Intelligent Transportation Systems

The independent metering system decouples the meter-in and meter-out flows of the chamber, giving extra control flexibility and can reducing energy consumption while keeping motion control accuracy. The control performance of the independent metering system is significantly determined by the valve characteristics. Valve nonlinearities, such as deadband, nonlinear flow gain, and leakage, may restrict the control accuracy. To address the issue and improve system control precision, the nonlinearities of the valve need to be further modeled. In this study, a nonlinear valve flow model is proposed to accurately depict the relationships between the flow rate, pressure drop, and input voltage. The valve deadband is compensated by the static inverse function, while a certain polynomial projection function is used to mimic the nonlinear flow curve outside the deadband. To deal with uncertainties and nonlinearities in the independent metering system, an adaptive robust control approach is synthesized. The least squares estimation law is adopted to online adapt the valve parameter and other system parameters. Comparative experiments were carried out to illustrate the effectiveness of the proposed approach. The results show that the valve flow nonlinearities are further captured by the proposed model, and the independent metering system performed a higher-level control precision.

This article proposes a novel gain-scheduling control method to improve vehicle lateral stability based on a variable-parameter-dependent approach. A time-varying velocity-dependent model to describe the vehicle lateral dynamic characteristics is constructed under cornering stiffness uncertainties and controller saturation. A novel Lyapunov function with variable-parameter-dependent Lyapunov matrix is established to develop the conditions. Using the proposed Lyapunov function, a general condition of the variable-parameter-dependent saturated robust yaw moment controller is provided in terms of time-varying parameter-dependent matrix inequalities. In order to obtain a tractable solution, a condition is further developed with finite linear matrix inequalities. Moreover, an optimal distribution method is adopted to generate the desired yaw moment based on torque allocation. These torques are computed by optimizing the distribution errors and tire workloads. Simulations results under both J-turn and double-lane changing scenarios are used to illustrate the merits of the proposed method. The control synthesis approach is also applicable to other applications involving time-varying parameters.

A pneumatic artificial muscle (PAM) based on a metal hydride (MH) is considered for a compact compliant actuator. It is suitable for board applications of human robot interaction (HRI). To address the problem of HRI representing by varying environment, a compliant control is introduced. In fact, the bottlenecks of improving the performance in the compliant control of the PAM actuator are: a) an inherent non-linear dynamics of a PAM, b) the parametric and non-linear uncertainties, influenced by varying environment, and c) an additional high dimension introduced by an MH employed as a driving force for the PAM. We propose a learning-based adaptive robust control (LARC) framework to tackle these challenges. A Bayesian learning technique deals with the parameter adaptation for the adaptive control. The effectiveness of the LARC has been examined in extensive experiments of tracking control.

A multivariable robust control design for aircraft engines is proposed. The engine is modeled as a fuzzy dynamic system (FDS), which is not the same as Takagi-Sugeno inference system, based on a series of state vector models in the flight envelope. The possible value of uncertainty is prescribed to be within fuzzy sets. The uncertainty is divided into the matched and the mismatched portions. While the matched uncertainty lies within the range space of the input matrix, the mismatched uncertainty falls outside, which poses a significant challenge for control design. A robust control, which is deterministic and is not IF-THEN fuzzy rule based, is designed. The control design parameter needs to be feasible, i.e., within a prescribed range. Some prescribed deterministic performances of the system are guaranteed under the control, regardless of the uncertainty. By taking the control cost and the performance threshold into consideration, which is under the influence of both matched and mismatched uncertainty, the optimal choice of the control parameter is explored. As a result, this control design delicately blends optimality with mismatched uncertainty. This design is applied to a turbofan engine. HIL (hardware-in-the-loop) laboratory testing in the flight envelope demonstrates the superiority of the control design.

High dynamic tracking performance is a key technical index of hydraulic flight motion simulator (HFMS). However, the strong nonlinearities, various model uncertainties and measurement noise in hydraulic actuation systems limit the high dynamic performance improvement. In this paper, the outer axis frame of a HFMS is taken as a case study and its nonlinear dynamic model with consideration of strong nonlinearities, matched and mismatched uncertainties is established. A novel cascaded extended state observer (ESO) is proposed to estimate the unavailable system states to avoid the adverse effect of measurement noise on control performance. Meanwhile, the designed cascaded ESO also produces estimates of matched and mismatched uncertainties. Then, an output feedback robust controller (OFRC) is proposed by integrating the cascaded ESO with a robust integral of the sign of the error (RISE) feedback based on the backstepping framework. The proposed controller achieves compensation of both matched and mismatched model uncertainties in an output feedback form. Theoretical analysis indicates that the proposed OFRC ensures the boundedness of all closed-loop system signals in the presence of matched and mismatched time-varying model uncertainties. Excellent asymptotic tracking performance can also be obtained when the model uncertainties are time-invariant. Comparative experimental results show that the proposed OFRC achieves significant performance improvement compared with the extensively employed PI control with velocity feedforward (VFPI).

We propose a control approach for fully actuated mechanical systems using interval arithmetic, which guarantees global uniform ultimate boundedness of the tracking error and robust performance despite model uncertainties and input disturbances. Existing robust control methods often require computationally expensive or empirical estimations of bounds of state-dependent, nonlinear perturbations, arising from model mismatches. Our robust feedback control approach is different and removes these difficulties by using interval arithmetic to determine online the worst case perturbation acting on the error dynamics. We present two interval-arithmetic-based robust controllers by robustifying inverse-dynamics and passivity-based nominal control schemes. The effectiveness of our approach is demonstrated on a real robot manipulator with uncertain dynamics.

In this article, we investigate the problem of practical output regulation, i.e., to design a controller that brings the system output in the vicinity of a desired target value while keeping the other variables bounded. We consider uncertain systems that are possibly nonlinear and the uncertainty of their linear parts is modeled element wise through a parametric family of matrix boxes. An optimization-based design procedure is proposed that delivers a continuous-time control and estimates the maximal regulation error. We also analyze an event-triggered emulation of this controller, which can be implemented on a digital platform, along with an explicit estimate of the regulation error.

This article investigates the event-triggered output consensus problem for a class of unknown heterogeneous discrete-time linear multiagent systems in the presence of unmodeled dynamics. The agents have individual nominal dynamics with unknown parameters, and the unmodeled dynamics are in the form of multiplicative perturbations. A novel design framework is developed based on an event-triggered internal reference model and a distributed model reference adaptive controller. To deal with the heterogeneity of the multiagent system, the event-triggered internal reference model is designed to generate a virtual reference signal for each agent with a dynamic event-triggering mechanism being adopted to reduce the communication burden between neighboring agents. To handle the unknown parameters and unmodeled dynamics, the robust model reference adaptive controller is then designed to follow the generated virtual reference signal. It is shown that if the unmodeled dynamics satisfy certain conditions, then the boundedness of all the signals and variables in the closed-loop system and convergence of consensus errors to a residual set are guaranteed. Moreover, the consensus errors will converge to zero asymptotically in the absence of unmodeled dynamics. Compared with existing related works, the proposed framework is able to deal with the agents with individual unknown nominal dynamics and unmodeled dynamics. Moreover, the proposed framework is fully distributed in the sense that no knowledge of any global information is needed. Finally, the performance of the proposed method is validated by examples.

The required suitably soft-contact interaction in certain surgical device applications brings great challenges on the force and position control because the soft-contact environment is nonlinear, viscoelastic, and inhomogeneous. In this paper, a novel adaptive robust control approach, namely adaptive integral terminal sliding-mode-based impedance control (AITSMIC), is formulated to simultaneously regulate and control the position and force for a piezo-actuated ear surgical device with soft interaction. Firstly, the target impedance's steady-state performance is discussed by utilizing the nonlinear Hunt-Crossley model. To achieve the desired impedance, an integral terminal sliding manifold based on the auxiliary variable containing the impedance error is proposed to improve tracking performance and obtain the required finite-time convergence. Furthermore, an adaptive law is designed to get rid of system nonlinearities, uncertainties and disturbances, and to retain high robustness. The stability of the proposed control system is proven via the Lyapunov theory. Significantly, implementing the AITSMIC is straightforward, where only essentially one uniform controller is applied. Finally, several experiments are conducted to evaluate the effects of associated impedance parameters, verify the force tracking performance and validate the suitably practical application of AITSMIC on the procedure of ear surgery with soft interaction. The results show that excellent tracking performance and successful operation are achieved by the proposed controller.

International audience; This work addresses the problem of robust output feedback model predictive control for discrete-time, constrained, linear parameter-varying systems subject to (bounded) state and measurement disturbances. The vector of scheduling parameters is assumed to be an unmeasurable signal taking values in a given compact set. The proposed controller incorporates an interval observer, that uses the available measurement to update the setmembership estimation of the states, and an interval predictor, used in the prediction step of the MPC algorithm. The resulting MPC scheme offers guarantees on recursive feasibility, constraint satisfaction, and input-to-state stability in the terminal set. Furthermore, this novel algorithm shows low computation complexity and ease of implementation (similar to conventional MPC schemes).

Permanent magnet synchronous motor (PMSM) is widely used in electric vehicles due to its high power density. New requirements are constantly proposed with the development of PMSM, one of which is torque ripple. Current harmonic injection is a common method to minimize torque ripple. Designing effective controller to realize current harmonic injection is the key technology. In this paper, the transient voltage-current coupling equation considering magnetic saturation is derived by introducing incremental inductance. After appropriately simplifying, it is shown in form of the harmonic state space (HSS) equation. Considering that PMSM parameters varies with current due to magnetic saturation, robust controller is adopted to ensure stability. In order to eliminate the influence of motor speed change on control stability, the HSS is transformed into a spatial form. Then the speed adaptive robust (SAR) controller is designed. At last, the SAR controller is used in simulation and test bench experiment to verify dynamic response and stability. Compared with traditional PI and PR controller, the SAR controller can ensure good dynamic response, steady-state error and robust stability when speed and PMSM parameters vary. Moreover, SAR controller can well resist the harmonic coupling effect and system lag.

Uncertainty is a major concern in vehicle path tracking control design. The coefficients of the uncertainty bound are unknown. They are assumed to lie within prescribed fuzzy sets. First, based on the path tracking kinematic model, this paper innovatively formulates the vehicle path tracking task as a constraint-following problem. Second, we put forward a deterministic adaptive robust control law with a tunable parameter to ensure the uniform boundedness and ultimate uniform boundedness of the closed-loop system. Third, an optimal scheme for the tunable parameter is proposed based on the fuzzy uncertainty. The resulting optimal robust control (ORC) minimizes a comprehensive fuzzy performance index that involves the fuzzy system performance and the control cost. The results of the CarSim-Simulink co-simulation and the Hardware-in-loop (HIL) experiment together show that the proposed optimal robust control exhibits a superior path tracking performance.

This paper develops a novel decentralized controller for multi-area secondary load frequency control (LFC) of power systems. The proposed robust-adaptive approach estimates the external disturbance input and uncertainties, which are assumed to be matched with the control input. In this regard, a disturbance-observer state-feedback controller is designed. To offer a systematic approach, controller design conditions are derived in terms of linear matrix inequality (LMI) constraints. Thereby, for any given representation of the LFC area, the controller gains can be straightforwardly obtained by using numerical solvers. Moreover, in order to enhance the steady-state performance, the controller is modified through the heuristic genetic algorithm (GA). The controller design procedure is wholly offline and can be simply implemented. The developed decentralized approach does not need the information of the other areas, which reduces the cost and the number of measuring units. It is also robust against the power fluctuations of the load and renewable energy sources. To show the superiorities of the developed controller, four scenarios are considered. These scenarios comprise the aggregation of the photovoltaic, wind turbines, and electric vehicle (EV) to the power system. OPAL-RT experiments are given to verify the transient and steady-state performance and robustness of the proposed controller.

This article deals with the distributed H∞ robust control problem for linear multiagent systems perturbed by external disturbances and norm-bounded uncertain parameters over the Markovian randomly switching communication topologies. To tackle this problem, the distributed observer-based controller is proposed, which requires the relative information between neighbors and the absolute information of a subset of the nodes, and thus is intrinsically distributed. It is of great interest to see that the distributed H∞ robust control problem governed by such a controller can be converted to the stabilization with H∞ disturbance attenuation problems of some decoupled linear systems, whose dimensions equal those of a single node. Then, the H∞ stochastic robust performance region is defined to indicate the robustness of this controller against the variation of communication topologies. It is theoretically shown that the distributed observer-based controller yields bounded and connected robust performance region. Finally, the theoretical results are verified by conducting numerical simulations and experiments.

This paper provides two bounded finite-time control strategies for the stabilization problem of Euler-Lagrange (EL) systems exposed to actuator failures. By the combination of sliding mode technology and adaptive method, two control architectures have been constructed such that the system states will be forced towards the origin within finite time. The first controller is applicable in the case that exact information of the external disturbance and actuator faults are available. However, it still remains challenging for designers to obtain this sort of information in engineering practice. On account for this, adaptive laws are applied in the second controller to obtain estimations about the unknown parameters, thus ensuring desirable fault-tolerance ability and robustness for the EL systems. By resorting to the properties of EL systems and hyperbolic tangent functions, outputs of these two controllers will be proven to be bounded. Simulation examples are presented to manifest the validity of the developed algorithms.

The control problem of active suspension systems (ASSs) with uncertainties is considered by formulating control goals as a series of equality constraints (i.e., soft constraints) and inequality constraints (i.e., hard constraints). Uncertainties are (possibly fast) time-varying, bounded and include large mismatched portions. However, bounds are unknown. The objective is to design an adaptive robust control driving the system to converge to soft constraints provided by sky-hook model and simultaneously ensuring the system to meet hard constraints at every instant. The adaptive robust control design is implemented in four steps. First, we investigate a transformation technique for incorporating hard constraints into soft constraints and the model. Second, a nominal control is presented without considering uncertainty. Third, an orthogonal decomposition technique is proposed for dividing uncertainty into matched and mismatched portions, which creatively allocates the mismatched portion for later control design. Fourth, a continuous adaptive law is constructed to emulate a constant design parameter vector associated with uncertainty bounds. It is proved that the proposed control guarantees uniform boundedness and uniform ultimate boundedness of ASSs in the presence of uncertainties and hard constrains. Furthermore, experimental and simulation results on 2-DOF ASS are presented to validate the effectiveness of the proposed control.

While designing control for a class of underactuated mechanical systems (UMSs), the uncertainty and the prescribed nonholonomic tracking trajectories should be taken into consideration. Uncertainty considered in this article is time varying and bounded, and the bound of uncertainty is described using the fuzzy set theory, namely, fuzzy UMSs. An analytical dynamics-based view is taken in which the prescribed tracking trajectories are viewed as servo constraints which can be linear, nonlinear, holonomic, and nonholonomic. Using this view, a novel closed form solution of adaptive robust control is found with leakage type adaptive law to guarantee deterministic system performance, including uniform boundedness and uniform ultimate boundedness. In order to find the optimal dual gain parameters of the designed control, a two-player cooperative game is proposed for which the Pareto optimality can always be guaranteed. The effectiveness of the proposed control is shown through numerical simulation of a two-wheeled inverted pendulum vehicle.

This paper presents the design, implementation, and validation of a novel robust control strategy based on variables transformation, i.e., transforming variables to obtain the triangular flat canonical normal form (TCNF) for nonlinear dynamic systems satisfying the flatness geometric property. A differential flatness, integrated with a geometrical transformation-based method, was developed to control an exoskeleton robot named Smart Robotic Exoskeleton (SREx). The SREx was designed to provide upper limb rehabilitation therapy to the stroke survivors. The proposed flatness control technique ensures continuous enhanced trajectory tracking and the system's high robustness during following a trajectory representing rehabilitation exercises. Furthermore, utilizing the Lyapunov theory, all signals were shown to be bounded in the closed-loop form. Experiments and comparative studies were carried out to validate the effectiveness of the proposed control scheme. Controlled experiments were further conducted using healthy subjects, maneuvering the SERx to provide rehabilitation exercise and to validate the control scheme in real-time.

In a typical wireless power transfer (WPT) system, the load, the mutual inductance and the required tuning frequency can vary in a particular range. Variation of each parameter can substantially impact the dynamic characteristics of the system. Thus, they can be considered as the sources of uncertainty in the system. To address this issue, robust control methods such as -synthesis are developed to deal with possible system uncertainties. In this paper, first, the generic dynamic analysis of the series-series WPT compensation network for two modes of operation, i.e. Constant Output Voltage (COV) mode and Constant Output Current (COC) mode, in the presence of three aforementioned uncertainty sources is carried out. Subsequently, the frequency detuning as a function of the compensation capacitor variation is explored and broadened as a technique to obtain the optimized compensation capacitor value that can lead to a plant with minimized dynamic deviations from its nominal system in the operating range between COC and COV modes. As such, this approach offers a design procedure for a least conservative robust controller which can significantly improve the system performance. The optimized structure and the corresponding designed -synthesis controller are comprehensively elaborated.

This paper concentrates on a simple and robust control method for the discrete time nonlinear systems to fulfill the requirement of predefined accuracy. A sliding mode control method is designed by introducing equivalent dynamic linearization technique according to the input/output (I/O) information merely. A square-root type error transformation method is presented for the tracking error to be restricted within a preassigned zone. The performance of presented control method is demonstrated through experiments on a nonlinear system. Experiment results show that the presented control method has a superior tracking accuracy compared with PID controller and model-free adaptive control (MFAC).

International audience; In this paper a robust nonlinear Model Reference Adaptive Control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of Linear Matrix Inequalities (LMIs). Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than the provided by a classic MRAC.

Deep implicit models are very recent developments on deep learning. Traditionally, deeplearning methods rely on explicit forward feeding structures. Super deep structures are proposed to give better performance in various domains. Such approaches have posed difficultyin theoretical analysis and under perform shallower models in some domains. By introducinga recursive structure involving solution to an equilibrium equation in the forward feeding,implicit deep models capture the idea of infinitely deep neural networks while preservingsimplicity in model representation, allowing theoretical analysis and better connection toprevious efforts in math and control communities. Recent works on implicit models havedemonstrated state-of-the-art empirical performances.Despite great ambition, implicit models are very new and see theoretical and empiricalchallenges. From the theoretical aspect, efficient and effective training and evaluation ofimplicit models are still open problems. The naive training methods for implicit modelsare highly inefficient. Trivial initialization easily violates the validity conditions for implicitmodels. Robustness of implicit models are not well studied. From the empirical aspect, thereare still a limited number of works on applying implicit models to solve real world problems.Such works also have not demonstrated significant performance boost over deep learning ingeneral. Applications of implicit models in most areas are mostly unexplored even thoughimplicit models fit in the deep learning framework easily.In the dissertation, we introduce our theoretical and empirical contributions on deep implicitmodels. The presentation of the dissertation is split into two parts. The first part focuses ontheoretical foundations for deep implicit models where we research the evaluation, training,and other topics for implicit deep learning and deep learning in general. The second partthen explores the applications of deep implicit models and corresponding theories on realworld machine learning applications. We show that implicit models can out-perform existingdeep learning techniques in a set of tasks, thanks to the implicit structure which resemblesinfinitely deep neural networks.

As the systems we control become more complex, first-principle modeling becomes either impossible or intractable, motivating the use of machine learning techniques for the control of systems with continuous action spaces. As impressive as the empirical success of these methods have been, strong theoretical guarantees of performance, safety, or robustness are few and far between. This manuscript takes a step towards such providing such guarantees by establishing finite-data performance guarantees for identifying and controlling fully- or partially-unknown dynamical systems.In this manuscript, we explore three different viewpoints that each provide different quantitative guarantees of performance. First, we present a generalization of the classical theory of integral quadratic constraints. This generalization leads to a tractable computational procedure for finding exponential stability certificates for partially-unknown feedback systems. Second, we present non-asymptotic lower and upper bounds for core problems in the field of system identification. Finally, using the recently developed system-level synthesis framework and tools from high-dimensional statistics, we establish finite-sample performance guarantees for robust output-feedback control of an unknown dynamical system.

Inherent nonlinearities and uncertainties are inseparable parts of the real-life engineering systems, which make theoretical analyzes and control system designs more challenging. Usually, most of the physical parts in control systems such as controllers and actuators are subjected to saturation. On the other hand, uncertainties are ubiquitous in the physical systems, which demand some necessities in the design of the control system. Additionally, unreliability in communication networks is another practical constraint in multiagent systems, which is required to be considered. In this article, based on the mentioned issues, a distributed robust algorithm is proposed for the semiglobal stabilization of the voltage and frequency of isolated (islanded) ac microgrids considering parameters uncertainties, static nonlinearity of actuators, and unreliability in the communication network. In this regard, by employing an adaptive low-gain feedback protocol, the robust performance of the closed-loop system is guaranteed. Finally, to evaluate the proposed control strategy’s performance, digital time-domain simulations are carried out on a test microgrid system in MATLAB/Simulink environment, and the results are compared with several previously reported methods. Simulation results and comparison with previous works reveal the proposed method’s effectiveness and accuracy in regulating the microgrid voltage/frequency and providing accurate proportional active power sharing.