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This article proposes an adaptive robust formation control scheme for the connected and autonomous vehicle (CAV) swarm system by utilizing swarm property, diffeomorphism transformation, and constraint following. The control design is processed by starting from a 2-D dynamics model with (possibly fast) time varying but bounded uncertainty. The uncertainty bounds are unknown. For compact formation, the CAV system is treated as an artificial swarm system, for which the ideal swarm performance is taken as a desired constraint. By this, formation control is converted into a problem of constraint following and then a performance measure β is defined as the control object to evaluate the constraint following error. For collision avoidance, a diffeomorphism transformation on space measure between two vehicles is creatively performed, by which the space measure is positive restricted. For uncertainty handling, an adaptive robust control scheme is proposed to render the β -measure to be uniformly bounded and uniformly ultimately bounded, that is, drive the controlled (CAV) swarm system to follow the desired constraint approximatively. As a result, the system can achieve the ideal swarm performance; thereout, compact formation is realized, regardless of the uncertainty. The main contribution of this article is exploring a 2-D formation control scheme for (CAV) swarm system under the consideration of collision avoidance and time-varying uncertainty.

This article addresses a cooperative game-oriented optimal constraint-following problem for fuzzy mechanical systems. The state of the concerned system is affected by possibly (fast) time-varying uncertainty. The fuzzy set theory is adopted to describe such uncertainty. The task is to drive the system to obey a set of prescribed constraints optimally. Since the control objective may be changing along with the system uncertainty, a time-varying β-measure is defined to gauge the constraint-following error; based on which, an adaptive robust control scheme with two tunable parameters is then proposed to render it to be uniform boundedness and uniform ultimate boundedness. For the seeking of the optimal design parameters, two cost functions, each of which is dominated by one tunable parameter, are developed with the fuzzy information, and thereout a two-player cooperative game is formulated. Finally, the optimal design problem is successfully solved: with the existence, uniqueness, and analytical expression of the Pareto optimality.

Pointing tracking control of marching turret-barrel system is one of the important topics in exploration of intelligent ground combat platform. This paper focuses on an adaptive robust control scheme for pointing tracking of marching turret-barrel system driven by a motor and an electric cylinder. Three types of possibly fast time-varying but bounded uncertainty are considered: system modeling error, external disturbance and road excitation. The uncertainty bounds are not necessary to be known. First, the pointing tracking system is constructed as a coupled, nonlinear and uncertain dynamical system with two interconnected (horizontal and vertical) subsystems. Second, a tracking error e is defined as a gauge of control objective, and then the dynamical equation of the pointing tracking system is built in state-space form. Third, for uncertainty control, a comprehensive uncertainty bound α is derived to measure the most conservative influence of the uncertainty, and then an adaptive law is proposed to evaluate it in real time. Finally, for pointing tracking control, an adaptive robust control is proposed to render the pointing tracking system to be practically stable; thereout, the objective of pointing tracking is achieved. This work should be among the first ever endeavours to cast all the coupling, nonlinearity and bound-unknown uncertainty into the pointing tracking framework of marching turret-barrel system.

This paper proposes an optimal parameter design of control scheme for mechanical systems by adopting the Stackelberg game theory. The goal of the control is to drive the mechanical system to follow the prescribed constraints. The system uncertainty is (possibly fast) time-varying and bounded. A β-measure is defined to gauge the performance. A robust control is proposed to render the β-measure uniformly ultimately bounded. This control scheme is based on feasible design parameters (i.e., parameters within prescribed range), and the choices of these parameters may not be unique. For optimal (unique) parameter selection, a Stackelberg game is formulated. By taking the control design parameters as the players, for each player, a cost function is built with the consideration of the performance cost, the time cost and the control cost. To follow, the Stackelberg strategy is then carried out via backward induction, which results in the choice of the optimal parameters.

This paper proposes a robust control approach to achieve high-precision trajectory tracking for permanent magnet linear motor (PMLM) system containing uncertainties by describing the dynamic model of PMLM based on the Udwadia-Kalaba equation combined with constraint-following method. First, the system of PMLM is described as a constraint-following system by adding the generalized constraint force to the unconstrained Udwadia-Kalaba equation of PMLM system. Second, the robust constraint-following controller is designed based on the proposed model after uncertainty analysis. Moreover, the proposed controller is verified to guarantee deterministic performance for uncertain systems: uniformly bounded and uniformly ultimately bounded. Third, the numerical simulation and experimental validation demonstrate the effectiveness of proposed controller. Finally, the design approach of constraint-following can be applied to other systems with uncertainties. [ABSTRACT FROM AUTHOR]

An air–ground heterogeneous unmanned swarm system coordination is considered. The system consists of N unmanned aerial vehicles (UAVs) and one unmanned ground vehicle (UGV). This forms a complicated mission, which consists of the following four different tasks. First, the aerial vehicles are in a compact formation, while avoiding collision with each other. Second, the aerial vehicles should stay close to the ground, while avoiding collision with the ground. Third, the aerial vehicles should stay close to the ground vehicle. Fourth, the ground vehicle should follow a desired trajectory. These tasks reflect two seemingly contradictory nature: close to (due to tracking) and away from (due to avoidance). The effective control design should address all four tasks even in the presence of uncertainty. By two creative transformations, this multitude of tasks are consolidated in a χ -measure. An adaptive robust control, which includes a robust control scheme and an online adaptation law, is then proposed to render guarantee boundedness performance of this χ -measure. As a result, the control design is able to accomplish the combined tracking-avoidance mission for the uncertain swarm system. Despite the presence of conflicting aspects between these tasks, the designed controller exhibits outstanding performance. • A multitasking control framework is proposed for air-ground coordinated systems. • Two contradictory tasks of tracking and avoidance are solved by one control method. • An adaptive robust control is designed for the systems with uncertainty. • Multiple performances of the systems are realized by one controller. [ABSTRACT FROM AUTHOR]

In this paper, a new practical dynamic robust control approach for cooperative robots with inequality constraints is proposed. The controller can compensate errors caused by uncertainties and external disturbances. The inequality constraint is eliminated by choosing proper boundary function and using state transformation. In this way, the controlled output is guaranteed within the desired range. The Lyapunov minimax method is used to prove that the controller can guarantee the uniform boundedness and uniform ultimate boundedness and stability of the robot system. Experimental verifications are carried out on a 2-DOF cooperative robot experimental platform with joint modules. The experimental platform is equipped with a rapid prototyping controller system (CSPACE). Numerical simulation and experimental verification results show that the proposed practical robust controller has significant advantages of trajectory tracking performance and security for cooperative robots with inequality constraints. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive robust control approach has been proposed for a class of uncertain mechanical systems. First, aiming for the unknown uncertainties which may be fast time-varying, a novel adaptive mechanism in leakage-type will be developed. Unlike the prevalent adaptive methods, this adaptive mechanism put forward mainly accounts for estimating all the lumped uncertainty terms, and does not require any information of uncertainties other than they are bounded; Second, through transforming the gait following assignment to the constraint control, an adaptive robust constraint-following controller constructed will render the constraints uniformly bounded and uniformly ultimately bounded. To testify the efficacy of proposed approach, a lower limb exoskeleton robot is considered as an illustrative example, the simulations indicate that the proposed control can indeed improve the level of passive rehabilitation training. [ABSTRACT FROM AUTHOR]

Based on the traditional PID control and robust control algorithm, a novel practical robust control method is designed for the 6‐DOF collaborative industrial robot with uncertainty. The proposed algorithm consists of a robust term and a model‐based PD control term, which we call MPDP controller. It is demonstrated by Lyapunov theoretical analysis that the algorithm is able to guarantee uniform boundedness and uniform ultimate boundedness of the system. Simulations and experiments show the good performance of MPDP control in a robot with smaller steady‐state tracking errors and better robustness compared to PID controllers. [ABSTRACT FROM AUTHOR]

In this paper, we design a novel robust control method to reduce the trajectory tracking errors of the SCARA robot with uncertainties including parameters such as uncertainty of the mechanical system and external disturbance, which are time-varying and nonlinear. Then, we propose a deterministic form of the model-based robust control algorithm to deal with the uncertainties. The proposed control algorithm is composed of two parts according to the assumed upper limit of the system uncertainties: one is the traditional proportional-derivative control, and the other is the robust control based on the Lyapunov method, which has the characteristics of model-based and error-based. The stability of the proposed control algorithm is proved by the Lyapunov method theoretically, which shows the system can maintain uniformly bounded and uniformly ultimately bounded. The experimental platform includes the rapid controller prototyping cSPACE, which is designed to reduce programming time and to improve the efficiency of the practical operation. Moreover, we adopt different friction models to investigate the effect of friction on robot performance in robot joints. Finally, numerical simulation and experimental results indicate that the control algorithm proposed in this paper has desired control performance on the SCARA robot. [ABSTRACT FROM AUTHOR]

Mechanical systems with (possibly fast) time-varying but bounded uncertainty are considered. The exact value of the boundary is unknown. All the designer can get is that the boundary values are in a (known) fuzzy set. On the basis, a robust control method is proposed, which can ensure the uniformly bounded and uniformly ultimately bounded of the controlled mechanical system. The control contains two flexibly selectable design parameters. We seek to choose the optimal parameters. For a superior performance, two fuzzy-set-based performance indices are proposed to reflect the transient performance as well as the steady-state performance. Each performance index can be influenced by two design parameters. However, influences are nonconciliatory. This poses a design dilemma: the increase of a parameter may harness one performance while inflict the other. Therefore, the “optimal” choice of the design parameters is not intuitively clear. To resolve this dilemma, the two-player Nash-based noncooperative game theory is adopted, which is a notable feature of this article. Once the problem is formulated, we show that there is always a Nash-equilibrium solution to the two-player problem. We also show how to find it. The approach is very general, which also can be extended to $n$ -player Nash game for future research. The control is applied to a compressor powered by permanent magnet synchronous motor (PMSM) as a demonstration. The resulting performance shows that this Nash-based robust control design is both practical and effective. [ABSTRACT FROM AUTHOR]

In recent years, there has been a great deal of interest in underwater sensor networks (UWSNs) because they can effectively monitor the submerged environment. However, due to the long delay, high bit error rate, and limited propagation bandwidth of underwater acoustic channels, the media access control (MAC) protocol cannot function effectively in underwater acoustic sensor networks, particularly in offshore waters. To solve these issues, an MAC protocol with time synchronization and power control (TSPC) is proposed for a particular scenario. In addition, the proposed protocol is a joint channel access scheme, and the central nodes are deployed on an offshore seabed, which can be used as a synchronization reference standard time. A power control strategy is also implemented to limit the communication range of nodes. In brief, integrating TSPC with layered concepts and distributed clustering algorithms can effectively prevent communication collisions and reduce the energy consumption of UWSNs. The simulation results indicate that the TSPC MAC protocol performs well with regard to packet transmission rate, synchronization error, collision-free operation, and energy consumption. [ABSTRACT FROM AUTHOR]

In this article, we apply a high-order control to a dynamical system with uncertainty. There are two characteristics. First, the uncertain part, which is time-varying but bounded, is described in a fuzzy aspect. Specifically, the uncertainty lies within a fuzzy set and the bound is regarded as a fuzzy number. Second, the systems are uniformly bounded and uniformly ultimately bounded with a deterministic controller based on the Lyapunov theory. To obtain better system performance and lower control input, we apply the noncooperative game theory to optimize the parameters by establishing a Nash game. Then, the D-operation is proposed for the uncertainty related to fuzzy numbers. Finally, we perform the numerical simulations of the steering-by-wire system for verification. [ABSTRACT FROM AUTHOR]

This article focuses on a robust control scheme for pointing control of the marching tank gun. Both matched and mismatched uncertainties, which may be nonlinear (possibly fast) time varying but bounded, are considered. First, the pointing control system is constructed as a coupled, nonlinear, and uncertain dynamical system with two interconnected (horizontal and vertical) subsystems. Second, for the horizontal pointing control, robust control is proposed to render the horizontal subsystem to be practically stable. Third, for the vertical pointing control, an uncertainty bound-based state transformation is constructed in a similar way of backstepping to convert the original mismatched system (i.e., the vertical subsystem) to be locally matched and then robust control is proposed to render the transformed system to be practically stable. Finally, it is proved that when the transformed system is rendered to be practically stable, the original system renders the same performance; therefore, vertical pointing control is achieved. This work should be among the first ever endeavor to cast all the coupling, nonlinearity, and (both matched and mismatched) uncertainty into the pointing control framework of the marching tank gun. [ABSTRACT FROM AUTHOR]

A novel robust control design is proposed for aircraft engines. The engine is modeled as an uncertain dynamic system, whose uncertainty may be (possibly fast) time-varying. The possible value of the uncertainty is prescribed to be within fuzzy sets. This distinguishes our modeling from the Takagi–Sugeno inference system. The uncertainty is divided into matched and 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 the control design. The objective is to propose a new robust control design for aircraft engines, which are subject to mismatched uncertainty. 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. By taking the control cost and the performance threshold into consideration, which is under the influence of both matched and mismatched uncertainty, the unique optimal choice of the design parameter is proposed. As a result, this control design delicately blends optimality with mismatched uncertainty. This design is applied to a turbofan engine. Hardware-in-the-loop laboratory testing in the flight envelope demonstrates the superiority of the control design. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article proposes an optimal indirect approach of constraint-following control for fuzzy mechanical systems. The system contains (possibly fast) time-varying uncertainty that lies in a fuzzy set. It aims at an optimal controller for the system to render bounded constraint-following error such that it can stay within a predetermined bound at all time and be sufficiently small eventually. First, for deterministic performance, the original system is transformed into a constructed system. A deterministic (not the usual IF-THEN rules-based) robust control is then designed for the constructed system to render it to be uniformly bounded and uniformly ultimately bounded, regardless of the uncertainty. Second, for optimal performance, a performance index, including the average fuzzy system performance and control effort, is proposed based on the fuzzy information. An optimal design problem associated with the control gain is then formulated and solved by minimizing the performance index. Finally, it is proved when the constructed system renders uniform boundedness and uniform ultimate boundedness, the original system achieves the desired performance of bounded constraint following. [ABSTRACT FROM AUTHOR]

In this paper, we study the constraints of control inputs, which is important to system performance, but rarely noticed. To deal with the constraints in practical situations, a new approach is proposed based on using diffeomorphism, which is the first introduced. Based on this transformation, the control input can be regarded as a function of an auxiliary variable. As a result, the value of control input is limited to a prescribed bound by choosing the proper bounded function. That is, it provides a new aspect to deal with the inequality control input constraints. The range of the input bounds is related to the uncertainties and can be designed according to the actual situation. This novel control is proven to guarantee uniform boundedness and uniform ultimate boundedness. In the simulation, we show this control renders a superior performance at a lower control cost, comparing with the LQR control. [ABSTRACT FROM AUTHOR]

In order to reduce the impact of load and system parameter changes on the dynamic performance of collaborative robot joint module, a novel robust control algorithm is proposed in this paper to solve the problem of dynamic control of collaborative robot joint module trajectory tracking. The controller is composed of two parts: one is a nominal control term designed based on the dynamical model, aiming to stabilize the nominal robot system; the other is a robust control term based on the Lyapunov method, aiming to eliminate the influence of uncertainty on tracking performance, where the uncertainties include nonlinear friction, parameter uncertainty, and external disturbances. The Lyapunov minimax method is adopted to prove that the system is uniformly bounded and uniformly ultimately bounded. We performed numerical simulation and experimental validation based on an actual collaborative robot joint module experimental platform and the rapid controller prototype cSPACE. The numerical simulation and experimental results show that the controller has excellent control performance for the collaborative robot joint module and provides more accurate trajectory tracking under the influence of uncertainties. [ABSTRACT FROM AUTHOR]

This article proposes a novel robust swing-up and balance control method using data-driven compensation signals for the Pendubot system, which is underactuated and subject to dynamic friction, backlash, and modeling uncertainty. The method involves three major developments. First, the uncertainty of the system is described by a previous sampled unknown nonlinear term and its changing rate. Compensation signals are then designed to eliminate the influence of the previous sampled unknown nonlinear term and its changing rate on the outputs of the controlled plant. Second, based on the Lyapunov stability theory, a robust swing-up control method is proposed. Third, in order to eliminate the limit cycle phenomenon caused by the uncertainty near the unstable equilibrium point, a proportional-derivative balance controller based on compensation signals is proposed. The stability and tracking error analysis show that the compensation signals can effectively eliminate the influence of dynamic friction, backlash, and modeling uncertainty on the system. Experimental results verify the effectiveness of the proposed method by showing significant improvements in production rate, accuracy, and cost. [ABSTRACT FROM AUTHOR]

A novel class of high-order robust controls is presented for uncertain fuzzy systems in this article. The optimal tunable parameters are also obtained based on the Stackelberg game theory. First, a dynamical system structure is formulated with uncertainty. The uncertain portion in the system is bounded, nonlinear, and time-varying which is within prescribed fuzzy set. Thus, this is a fuzzy system. Then, the proof based on the Lyapunov minimax approach shows that the novel high-order robust controls are able to assure deterministic system performance, which is uniform boundedness and ultimate uniform boundedness. Furthermore, the optimal choice of the tunable parameters in the control is considered. We creatively apply the Stackelberg strategy to solving the optimization problem. Two parameters are regarded as leader and follower in a sequential game, respectively. Based on the Stackelberg game rules, we are able to design different cost functions for different parameters. The cost functions include both performance measures and control cost. Finally, the simulations of an electronic throttle system are presented for demonstration. [ABSTRACT FROM AUTHOR]

In this article, we propose a high-order robust control for fuzzy dynamical systems. The time varying but bounded uncertainty in this system is described by the fuzzy set theory. The control is deterministic and is not based on IF-THEN fuzzy rules. By the Lyapunov approach, we prove that the control is able to guarantee uniform boundedness and uniform ultimate boundedness. In addition, the tunable parameters in the high-order control are regarded as two players in a cooperative game. Two cost functions are also proposed based on the two players. These two cost functions are related to system performance and control cost. Then, the optimal design problem is solved by finding the Pareto-optimality parameters. Numerical simulations are performed for verification [ABSTRACT FROM AUTHOR]

In this article, we are dedicated to coping with the control design for underactuated mechanical system (UMS) with system uncertainties, which is also subject to a set of servo constraints. For the nominal system without any initial condition deviations, this article provides a general model-based servo control with the idea of second-order constraints, which can be derived from both holonomic and nonholonomic ones. For the uncertain system, with the uncertainties being separated into matched portions and mismatched portions, this article provides an adaptive robust control scheme to guarantee the UMS to attain the deterministic performance on the basis of nominal control. The leakage-type adaptive law is to size up the unknown uncertainty bounds. The cart-pole system and the rotational-translational actuator system are used to verify the availability of the proposed adaptive robust control. [ABSTRACT FROM AUTHOR]

This article proposes a new robust control design framework for uncertain mechanical systems, which may be fully actuated or underactuated. The uncertainty is (possibly fast) time varying, which lies in prescribed fuzzy sets (hence fuzzy mechanical systems) and may be unbounded. The control goal is formulated as servo constraints (hence constraint-following control), which may be holonomic or nonholonomic. We introduce the possibility theory into the Lyapunov stability analysis (LSA), proposing possibility-based LSA (PBLSA), which allows a maximum failure possibility (generally small) prescribed by designers. It can be viewed as a generalization of the conventional LSA, and the resultant performance is interpreted in the context of possibility. By the PBLSA, a class of robust constraint-following controls that is not IF–THEN heuristic rules based is proposed, which renders approximate constraint following for the system performance with a prescribed maximal failure possibility. Optimal design of a control parameter considering both system performance and control cost is investigated. The benefits of the proposed design framework are discussed and simulations on two applications are given for demonstrations. [ABSTRACT FROM AUTHOR]

To enhance the lower limbs’ rehabilitation training of stroke patients, in this article, a deterministic adaptive robust control with control gain parameters optimized by a novel cooperative game theory is proposed for the two-degree-of-freedom (DOF) lower limb exoskeleton robot system (LLERs) with uncertainties and external disturbances. On the one hand, the deterministic adaptive robust control put forward will guarantee the uniform boundedness and uniform ultimate boundedness of gait constraint deviation and parameter estimation error. On the other hand, for uncertainties and external disturbance (possibly fast time-varying), which will arise in the two-DOF LLERs inevitably, we suppose that these uncertainties and disturbances are bounded, and their bounds are lying within the fuzzy sets, which can be characterized by membership functions; with such descriptions and control performance analysis, a novel cooperative game with two players participated will be formulated to seek the Pareto optimal solutions for the control gains of deterministic adaptive robust control proposed, and furthermore, the existence of optimal solutions is also shown by invoking a numerical technique. Eventually, the simulation results presented have verified the effectiveness of our proposed methodology on improving rehabilitation training of lower limbs. [ABSTRACT FROM AUTHOR]

This article addresses the control design problem for a fuzzy vehicular platoon system consisting of one leading vehicle and $N$ following vehicles. Due to external disturbances, uncertainty exists in the platoon system and is usually nonlinear and possibly fast time varying. In order to deal with uncertainty, fuzzy theory is employed to describe the platoon system, thereby the so-called fuzzy vehicular platoon system. Based on the fuzzy property of uncertainty, a type of adaptive law is proposed. Since the original state of the system is one-side bounded when collision avoidance is taken into account, a state transformation is made, by which a new global state is obtained. Then, the swarm intelligence is embedded into the platoon system via a function, which mimics the swarm behavior. For the control design, we focus on adaptiveness and optimization. A switching-type adaptive robust control is proposed. The control is not IF–THEN rule based. We further explore the problem of control parameter optimization. A performance index consisting of transient control cost and average control cost is proposed. Aiming at minimizing the performance index, the optimal problem is formulated. The solution to the optimal problem (i.e., optimal control parameter) exists and is unique. The control with optimal parameter is called optimal control, which guarantees both deterministic performance (uniform boundedness, uniform ultimate boundedness, and collision avoidance) and fuzzy performance of the platoon system. [ABSTRACT FROM AUTHOR]

Control design and performance enhancement for uncertain mechanical systems are pursued in this article. Uncertainty in a physical system is often inevitable in practice, which is best characterized by its possible bound. Mechanical systems with uncertain nonlinearity are considered. Furthermore, even the knowledge of the coefficients in the bound is unknown, which can only be described by its fuzzy association to a set. In controlling the system, there is a hierarchical performance requirement. The first level is deterministic, including uniform boundedness and uniform ultimate boundedness. This is the part the system must meet regardless of the actual value of the uncertainty. The second level is optimality, in terms of minimizing a fuzzy-theoretic performance index. We propose a novel control design with a tunable design parameter. The control guarantees the first-level performance when the design parameter falls in a range. We, then, take the advantage of this range flexibility to address the second-level requirement. The optimal choice of the design parameter can be made by solving an optimization problem. This problem is completely solved. Both the analytic (i.e., closed form) expressions of the design parameter and the resulting minimum cost are given. As a result, we accomplish a two-level control design task. [ABSTRACT FROM AUTHOR]

In this research, to achieve the altitude and attitude tracking control of an underactuated quadrotor UAV with mismatched uncertainties, based upon Udwadia–Kalaba theory, a novel adaptive robust tracking control approach is proposed and which will be designed in two steps. First, aiming at the uncertain and underactuated quadrotor UAV, regardless of initial constraint deviation and mismatched uncertainties, a nominal control is constructed through transforming the desired trajectories into corresponding servo constraints; second, for the mismatched uncertainties, we decompose them into two parts, i.e. the matched part and mismatched part, and the mismatched part will "vanish" during the stability analysis of proposed adaptive robust controller. Eventually, with such a decomposition technique, the large mismatched uncertainties can be addressed properly and the burden of controller design will be reduced to a certain degree. In addition, two deterministic robust control performances are also guaranteed by our proposed approach. The simulation results have shown a good robustness and tracking precision of our proposed scheme for quadrotor UAV. • The uncertainties have been decomposed into the matched and mismatched part. • A strong robustness against mismatched uncertainties is ensured by proposed scheme. • The mismatched part will "vanish" during the stability analysis of control system. • All the uncertainties have been lumped into two adaptive parameters. [ABSTRACT FROM AUTHOR]

This article proposes a novel robust control design for mechanical systems based on constraint following and multivariable optimization. The state of the concerned system is affected by (possibly fast) time-varying and bounded uncertainty. The objective is to drive the system to obey a set of prescribed constraints. A β-measure is defined to gauge the constraint-following error; based on which, a feedback robust control scheme, which invokes design parameters, is proposed. For the seeking of optimal design parameters, a multivariable constrained optimization problem is formulated. The problem is successfully solved: with the existence, uniqueness, and analytical expression (i.e., closed form) of the optimal design parameters demonstrated. With the optimal parameters, the proposed robust control can render dual performance: guaranteed and optimal. As the guaranteed performance, the β-measure is assured to be uniform boundedness and uniform ultimate boundedness. As the optimal performance, the performance index is globally minimized. This article is the first ever endeavour to cast both the constraint following and multivariable optimization into the control framework for uncertain mechanical systems. [ABSTRACT FROM AUTHOR]

A class of generalized nonlinear dynamic systems is first approximated by $N$ fuzzy-based linear subsystems using the identification of input–output data or the linearizing system with respect to suitable operating points. To obtain null trajectory tracking error in fixed time, a fuzzy fixed-time control (FFTC) with nonlinear switching surface and switching gain is first designed. It can be said that the FFTC is based on a class of passive and distributive models with uncertainties. To compensate enormous uncertainties, a fuzzy fixed-time learning control (FFTLC) by learning two unknown coefficients for the upper bound of uncertainties in each subsystem is designed. As compared with radial basis function neural network, the computational complexity for the compensated uncertainties is much simple. It can be said that an FFTLC is based on a class of online active and distributive uncertain models. Due to the fixed-time control design, the transients often occur, particularly for the larger uncertainties or initial tracking error. Hence, the saturated input of nonlinear dynamic system is addressed and online compensated. Finally, the compared simulations and application to two-link robot manipulator confirm the effectiveness, robustness, and less computation as compared with previous studies. [ABSTRACT FROM AUTHOR]

An optimal control design for the uncertain Delta robot is proposed in the paper. The uncertain factors of the Delta robot include the unknown dynamic parameters, the residual vibration disturbances and the nonlinear joints friction, which are (possibly fast) time-varying and bounded. A fuzzy set theoretic approach is creatively used to describe the system uncertainty. With the fuzzily depicted uncertainty, an adaptive robust control, based on the fuzzy dynamic model, is established. It designs an adaptation mechanism, consisting of the leakage term and the dead-zone, to estimate the uncertainty information. An optimal design is constructed for the Delta robot and solved by minimizing a fuzzy set-based performance index. Unlike the traditional fuzzy control methods (if-then rules-based), the proposed control scheme is deterministic and fuzzily optimized. It is proven that the global solution in the closed form for this optimal design always exists and is unique. This research provides the Delta parallel robot a novel optimal control to guarantee the system performance regardless of the uncertainty. The effectiveness of the proposed control is illustrated by a series of simulation experiments. The results reveal that the further applications in other robots are feasible. [ABSTRACT FROM AUTHOR]

This paper investigates the robust control for dynamical systems subject to uncertainty. The uncertainty is assumed to be (possibly fast) time varying and bounded. The bound is unknown but lies within a prescribed fuzzy set (hence the fuzzy dynamical system). We propose an approach for the robust control design which is implemented in two steps. First, a class of robust controls is proposed based on tunable parameters. The proposed controls are deterministic and are not conventionally IF-THEN rules based. By the Lyapunov minimax approach, we prove that the proposed controls are able to guarantee deterministic system performance, namely, uniform boundedness and ultimate uniform boundedness. Second, optima seeking from the proposed controls is considered to improve fuzzy system performance. We formulate the optima-seeking problem as a two-player (one leader and one follower) Stackelberg game by developing two cost functions, each of which is in charge of one tunable parameter (i.e., the player). Each cost function consists of an average fuzzy system performance index and the associated player’s control effort. We show that the solution of the optimal design problem (i.e., the optima of the tunable parameters), which is called the Stackelberg strategy, always exists and how to obtain the backwards-induction outcome is provided. Simulation results on the walking control of a biped robot model are presented for demonstration. [ABSTRACT FROM AUTHOR]

• The control problem of a soft robotic snake is for mulated as constraint following. • An adaptive robust control is designed for the soft robotic snake. • A smooth zone approach is proposed to construct the adaptation law. • Advantages of smooth zone approach over dead zone approach are demonstrated. This paper targets the motion control problem of a soft robotic snake with uncertainty. The problem is formulated as constraint-following. From practical point of view, the uncertainty is assumed to be (possibly fast) time-varying and bounded. The bound is unknown. To render constraint-following for the soft robotic snake, a new adaptive robust control is designed based on a novel design of the adaptation law. A smooth-zone approach is proposed to construct the adaptation law. Compared with the past discontinuous (hence non-smooth) dead-zone approach, the proposed approach ensures the adaptation law to be, besides saving control effort, continuous so that the adaptive parameters can vary smoothly, which in turn assures a smooth robot operation. We demonstrate that, even in the presence of uncertainty, the proposed control is capable of rendering approximate constraint-following by guaranteeing uniform boundedness and uniform ultimate boundedness. Simulation results on the soft robotic snake demonstrate the effectiveness and advantages of the proposed control. [ABSTRACT FROM AUTHOR]

The position control and vibration suppression problems of the flexible solar array drive system containing uncertainty are considered in this paper. The uncertainty in system may be due to unknown parameters and external disturbance. The uncertainty bound can be described via a fuzzy set. In addition, there exists the flexible vibration in the system. A new optimal robust control approach with input shaping is proposed for the flexible solar array drive system. By designing the position command trajectory, the input shaper is proposed to suppress the flexible vibration. To enhance the position control performance, the optimal robust control is proposed by fuzzy description of the uncertainty bound. Neither the system nor the control is fuzzy if–then rule based. The global solution to this optimal design problem is demonstrated to be always existent and unique. The resulting control is able to guarantee the uniform boundedness and uniform ultimate boundedness of the system in the presence of uncertainty, while minimizing a fuzzy-based performance index associated with both the fuzzy performance and the control cost. In addition, the flexible vibration can be effectively suppressed. The novelty of this research is a systematic control approach by blending input shaping technology, control theory, fuzzy set theory, and optimization theory into an integrated framework, for solving the position control and vibration suppression problems of flexible solar array drive system with mismatched conditions. [ABSTRACT FROM AUTHOR]

This study investigates the robust control for uncertain dynamical systems. The uncertainty is (possibly fast) time-varying but bounded. We adopt the fuzzy set theory to describe the uncertainty in the system (hence, called the fuzzy dynamical system). A class of robust controls is proposed based on tunable parameters. The controls are deterministic and are not conventional IF–THEN fuzzy rules based (such as Mamdani type). The proposed controls are able to guarantee deterministic system performance, namely uniform boundedness and uniform ultimate boundedness. In the phase of searching for the optima from the pool of admissible control design parameters, we formulate this as a two-player cooperative game by developing two performance indexes (i.e., the cost functions), each of which is dominated by one tunable parameter (i.e., the player). By the cooperative game theory, we are able to obtain the Pareto-optimality (i.e., the optima of tunable parameters). Simulation results on an electric vehicle motion control problem are presented for demonstration. [ABSTRACT FROM AUTHOR]

The robust control design problem for uncertain dynamical systems is considered in this study. The uncertainty is time varying (possibly fast) and bounded, and the bound lies within a prescribed fuzzy set (hence the fuzzy dynamical system). We design the robust control in two steps. First, we propose a class of robust controls based on tunable parameters, which is in deterministic form and not conventionally IF–THEN fuzzy rule based. It is shown that these controls are able to guarantee deterministic system performance, namely uniform boundedness and ultimate uniform boundedness. Second, we seek the optima of tunable parameters in the control by formulating a two-player Nash game, which is based on two performance indexes (i.e., the cost functions). It is shown that the Nash equilibrium (i.e., the optima of tunable parameters) always exists. The procedure of obtaining the Nash equilibrium is provided. Under the proposed control, the system performance is both deterministically guaranteed and fuzzily optimized from the Nash game perspective. The effectiveness of the control design is illustrated by the simulation control of a unicycle robot. [ABSTRACT FROM AUTHOR]

To achieve the state estimation of uncertain nonlinear systems, this paper proposes a novel optimal robust observer via the fuzzy bound information of the uncertainty. A robust observer scheme is first proposed to guarantee the uniform boundedness and uniform ultimate boundedness of the state estimation system regardless of the actual value of the uncertainty. To optimize the observer gain, a fuzzy set-theoretic-based optimal approach is then proposed by utilizing the fuzzy information of the uncertainty bound. The optimization problem is completely solved in analytic form. The resulting observer is able to guarantee the robustness of the state estimation system to the uncertainty, while minimizing an optimization index related to the state estimation performance and the observer cost. The novelty of this research is a creative optimal robust observer design by blending state estimation theory, fuzzy set theory, and optimization theory into an integrated framework. [ABSTRACT FROM AUTHOR]

The optimal design problem of adaptive robust control for fuzzy mechanical systems with uncertainty is investigated in this paper. The uncertainty that may be nonlinear and (possibly fast) time-varying is assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. Based on the Udwadia and Kalaba's approach, an adaptive robust controller, which is deterministic and is not the usual if-then rules-based is proposed to render the system to follow a class of prespecified constraints approximately. The adaptive law is of leakage type that can adjust the magnitude of the adaptive parameter based on the nonlinear performance-dependent gain. The resulting controlled system is uniformly bounded and uniformly ultimately bounded, which is proved via the Lyapunov minimax approach. Furthermore, we propose a novel concept: fuzzy confidence to measure the expectation value of a fuzzy number. Then, a fuzzy-based system performance index that includes the expectation value of the uniform ultimate boundedness (the average fuzzy performance) and the control cost is formulated. The optimal design problem associated with the control can then be solved by minimizing the performance index. As a result, the performance of the fuzzy mechanical system is both deterministically guaranteed and fuzzily optimized under this control. [ABSTRACT FROM AUTHOR]

This paper considers global asymptotic stabilization in probability for a class of cascaded stochastic nonlinear systems. The uncertainties do not meet the general matched conditions, and only boundedness of the uncertainties is assumed. Drawing on the stochastic asymptotic stability theorem, a novel robust controller is constructed based on the state transformation technique and the gradient method, which ensures that the closed-loop systems are globally asymptotically stable in probability. A numerical example is given to illustrate the effectiveness of the result. [ABSTRACT FROM AUTHOR]

We consider an uncertain mechanical system. The uncertainty includes the initial condition and system parameter. The uncertain parameter in the system is (possibly fast) time varying. The only known information about the uncertainty is that it lies in a fuzzy set. The mechanical system is to follow a set of constraints, which may include many engineering applications, even in the presence of uncertainty. For this purpose, we propose a $\beta$-measure for constraint obedience, which reflects how much this constraint is obeyed. Based on a very general Lyapunov function, a control scheme is proposed to render a twofold performance: guaranteed and optimal. In the guaranteed phase, the $\beta$-measure is assured to be uniformly bounded and uniformly ultimately bounded, regardless of the actual value of the uncertainty. In the optimal phase, a fuzzy-theoretic-based performance, by which both the “average” $\beta$-measure and control effort are considered, is minimized. As a result, the control serves the practical engineering purposes: The mechanical system is guaranteed to follow the desired task with the minimum cost. This paper is part of a unique endeavor to cast both the descriptions of the uncertainty and desired performance index into a fuzzy framework. [ABSTRACT FROM AUTHOR]

This article proposes a (cooperative) triple evasion-tracing-arrival problem for mechanical systems. The system contains uncertainty which is (possibly fast) time-varying but bounded; however, the bound is unknown. The main objective is to obtain controllers for the controlled system to assure three categories of system performance: evasion (with respect to a region), tracing (with respect to another region) and arrival (with respect to other another region). This problem is transferred as constraint-following control, based on which, the constraint derived from the original problem is creatively divided into two categories: evasion-tracing constraint and arrival constraint. Then, an adaptive robust control is designed, with which the evasion-tracing constraint is completely followed and the arrival constraint is closely followed by the system, regardless of the uncertainty. As a result, the triple evasion-tracing-arrival problem is solved. [ABSTRACT FROM AUTHOR]

Intelligent transportation has become an essential field of cyber-physical systems. Among various intelligent transportation technologies, the automated highway system (AHS) has its unique advantage of being able to coordinate a platoon of vehicles as a whole unit. The major challenge of building a robust AHS is the nonlinear and (potentially) fast time-varying uncertainty induced by parameter variations and external disturbances. Finally, reflected as the spacing between neighboring vehicles, such uncertainties can be a serious concern for maintaining safety. This paper addresses the problem by proposing a mathematical transformation scheme to bound the spacing error and build a distributed control algorithm on such a basis. The propose algorithm achieves a spacing error satisfying both uniformly boundedness and uniformly ultimate boundedness. Our decentralized algorithm is communication efficient in the sense that it only requires the state information of the preceding car and the acceleration feedback and does not need to communicate with all other cars. [ABSTRACT FROM PUBLISHER]

The control problem for a mechanical system to follow a constraint is formulated. The uncertainty is considered in both the system dynamics and constraint. It is bounded, and the knowledge of the bound only lies within a fuzzy set. We propose an adaptive robust control for the mechanical system for approximate constraint-following. Both the mechanical system model and control scheme are deterministic and not if–then heuristic rules-based. An optimal design problem using the fuzzy description of the uncertainty is proposed. We prove that the global solution to the resulting optimization problem always exists and is unique. Under the control, the performance of the mechanical system is both deterministically guaranteed and fuzzily optimized. [ABSTRACT FROM PUBLISHER]