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This paper addresses the inverse optimal security control problems for a class of stochastic non-strict feedback nonlinear cyber-physical systems under sensor and actuator attacks. The concerned system model includes both stochastic disturbances and more general nonlinearity. First, to make the control design feasible, a linear state transformation is applied to the attacked system. Furthermore, in the process of backstepping design, based on the Nussbaum gain function formula, fuzzy logic system approximation method, and inverse optimal control theory, combing the available output signal, an output feedback inverse optimal controller is proposed. Specifically, the designed controller not only ensures that the system is secure under network attacks but also optimal in terms of the cost function. Finally, two physical examples are given to verify the effectiveness of the proposed control scheme in various network attacks. [ABSTRACT FROM AUTHOR]

This article investigates the problem of inverse optimal fixed-time tracking for nonlinear switched systems. Given this, a control scheme is developed based on an adaptive direct fuzzy inverse optimal and fixed time. The proposed control strategy accomplishes optimal performance without solutions for the Hamiltonian function. On the other hand, this scheme designs inverse optimal controller and virtual controller without involving partial differential derivative terms, using a one-parameter learning mechanism so that the time difference of the Lyapunov function is non-positive. Two common Lyapunov function candidates are employed to demonstrate that the proposed control scheme stabilizes the switched system and the tracking error converges to a predefined region. [ABSTRACT FROM AUTHOR]

In addition to stability, the system optimality has also received attention because the system is expected to achieve higher performance with lower energy consumption. In general, the conventional approach to achieve optimal control of nonlinear MIMO systems is to solve the Hamilton–Jacobi–Bellman equation directly, which is time-consuming and sometimes impossible. To address this issue, this paper proposes an adaptive neural inverse optimal control method for uncertain MIMO systems. The method is based on an improved design criterion for the inverse optimal controller, which avoids the need for constructing auxiliary systems and enables direct stability analysis of MIMO systems. Additionally, an adaptive one-parameter update strategy is proposed to reduce the computational effort, which avoids the need to update the entire neural network. The proposed scheme guarantees that the tracking errors of the MIMO system converge to a given domain while minimizing a family of meaningful loss functions. Finally, the effectiveness of the presented method is verified through simulations. [ABSTRACT FROM AUTHOR]

Summary: In this article, for a class of stochastic nonlinear systems with non‐strict feedback, a neural adaptive inverse optimal output feedback control design scheme is presented. First, according to the existing inverse optimal criterion, an auxiliary system is established. On this basis, a novel observer is built to evaluate the unpredictable states. Second, in the control process, neural networks (NNs) are applied to estimate the unknown functions. Based on NNs and the backstepping technology, an adaptive neural inverse optimal output feedback controller is established. It is indicated that the proposed scheme could ensure the semi‐globally uniformly ultimately bounded of the closed‐loop system and also achieve the objective of inverse optimality. Eventually, an example is applied to testify the feasibility of this scheme. [ABSTRACT FROM AUTHOR]

A novel adaptive fuzzy predefined-time inverse approach is presented in this study, which enhances practical predefined-time stability to predefined-time stability. Unlike the existing optimal predefined-time control approaches, this method realizes the optimal performance without resolving the Hamilton–Jacobi–Bellman (HJB) equation, which simplifies the design and learning process. Firstly, by combining a Sontag-type function and a series of singularity-avoidance functions, an auxiliary controller is devised. Based upon this auxiliary controller, an inverse optimal predefined-time controller is set up. Secondly, based upon the method of two Lyapunov functions, it is demonstrated that the tracking error converges asymptotically to a predetermined interval within a predefined time and the inverse optimal stabilization is attained. Lastly, the availability of this method is testified through an example of the electromechanical system. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive speed control strategy for DC motors using a DC/DC converter (in buck and boost modes) based on the inverse optimal control (IOC) approach. Our proposal leverages the robust theoretical framework of IOC to derive a control law that ensures the stability and optimal performance of nonlinear dynamical systems through the Lyapunov theory. The control law is designed to minimize a specified cost function, implicitly supporting the optimality of the control strategy. An integral action is incorporated into the IOC approach to enhance performance, ensuring asymptotic stability without affecting convergence properties. The control strategy was implemented on buck and boost converter/DC motor systems. In addition, a disturbance observer technique was utilized for real-time load torque estimation, ensuring precise and efficient control to tackle the challenge posed by unknown and time-varying load torques. Simulations in PLECS and experimental results demonstrate the superiority of the proposed IOC approach compared to conventional cascaded PI control. Our approach reports significantly faster response times and reduced settling times in both buck and boost converter configurations, showcasing its potential for efficient and robust DC motor speed control applications.

Inverse optimal control is a method for recovering the cost function used in an optimal control problem in expert demonstrations. Most studies on inverse optimal control have focused on building the unknown cost function through the linear combination of given features with unknown cost weights, which are generally considered to be constant. However, in many real-world applications, the cost weights may vary over time. In this study, we propose an adaptive online inverse optimal control approach based on a neural-network approximation to address the challenge of recovering time-varying cost weights. We conduct a well-posedness analysis of the problem and suggest a condition for the adaptive goal, under which the weights of the neural network generated to achieve this adaptive goal are unique to the corresponding inverse optimal control problem. Furthermore, we propose an updating law for the weights of the neural network to ensure the stability of the convergence of the solutions. Finally, simulation results for an example linear system are presented to demonstrate the effectiveness of the proposed strategy. The proposed method is applicable to a wide range of problems requiring real-time inverse optimal control calculations. [ABSTRACT FROM AUTHOR]

To effectively suppress the longitudinal vibration of the car under the conditions of high-speed operation and emergency braking, and improve the ride comfort of the car system, this paper proposes an adaptive fuzzy inverse optimal output feedback control strategy. Firstly, the dynamic model of the high-speed elevator system is established and the nonlinear dynamic model is approximated by the fuzzy logic system, and the auxiliary system model is established. Fuzzy state observer is designed to estimate the unmeasurable state. Furthermore, an adaptive inverse optimal output feedback controller based on fuzzy observer is designed by using adaptive backstepping technology and inverse optimal control principle. The stability analysis shows that the proposed adaptive fuzzy inverse optimal output feedback control strategy not only ensures the stability of the car attitude of high-speed elevator but also realizes the inverse optimization of the target cost function. Finally, the acceleration time–frequency response analysis of the two typical stages of high-speed elevator uniform running and emergency braking is carried out, and the numerical results are compared with the linear quadratic controller optimized by stepping quantum genetic algorithm (GA-LQR) and controller based on the state-dependent Ricatti equation (SDRE). The analysis verifies the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

Robots deployed to the real world must be able to interact with other agents in their environment. Dynamic game theory provides a powerful mathematical framework for modeling scenarios in which agents have individual objectives and interactions evolve over time. However, a key limitation of such techniques is that they require a priori knowledge of all players' objectives. In this work, we address this issue by proposing a novel method for learning players' objectives in continuous dynamic games from noise-corrupted, partial state observations. Our approach learns objectives by coupling the estimation of unknown cost parameters of each player with inference of unobserved states and inputs through Nash equilibrium constraints. By coupling past state estimates with future state predictions, our approach is amenable to simultaneous online learning and prediction in receding horizon fashion. We demonstrate our method in several simulated traffic scenarios in which we recover players' preferences, for, e.g. desired travel speed and collision-avoidance behavior. Results show that our method reliably estimates game-theoretic models from noise-corrupted data that closely matches ground-truth objectives, consistently outperforming state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

Unknown model uncertainties and external disturbances widely exist in helicopter dynamics and bring adverse effects on control performance. Optimal control techniques have been extensively studied for helicopters, but these methods cannot effectively handle flight control problems since they are sensitive to uncertainties and disturbances. This paper proposes an observer‐based robust optimal control scheme that enables a helicopter to fly optimally and reduce the influence of unknown model uncertainties and external disturbances. A control Lyapunov function (CLF) is firstly constructed using the backstepping method, then Sontag's formula is utilized to design an inverse optimal controller to stabilize the nominal system. Furthermore, it is stressed that the radial basis function (RBF) neural network is introduced to establish an observer with adaptive laws, approximating and compensating for the unknown model uncertainties and external disturbances to enhance the robustness of the closed‐loop system. The uniform ultimate boundedness of the closed‐loop system is ensured using the presented control approach via Lyapunov stability analysis. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

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We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem. The reformulated problem is nonconvex and standard regularity conditions like Robinson's CQ are violated. Via a relaxation of the constraints, the problem can be decomposed into a family of convex problems and this is the basis for a solution algorithm. The convergence properties are analyzed. It is shown that a penalty method can be employed to solve this family of problems while maintaining convergence speed. For an example problem, the use of the identity as penalty function allows for the solution by a semismooth Newton method. Numerical results are presented. Difficulties and limitations of our approach to solve a nonconvex problem to global optimality are discussed. [ABSTRACT FROM AUTHOR]

In this study, a novel inverse optimal controller based on NARMA-L2 modelling technique and online least squares support vector regression (LSSVR) method has been proposed for nonlinear non-affine systems. Firstly, the nonlinear autoregressive with exogenous inputs (NARX) model of the system is obtained using online LSSVR method, then this model is decomposed into NARMA-L2 submodels. Hence, the non-affine system model is converted to a nonlinear affine system model. The obtained NARMA-L2 submodels are used in computing the inverse optimal control law. Furthermore, the parameters of the inverse optimal controller have also been optimized online using the Levenberg-Marquadt algorithm. The performance of the proposed LSSVR based inverse optimal controller using NARMA-L2 model has been evaluated by simulations carried out on two benchmark systems, and the results show that the LSSVR based NARMA-L2 model and inverse optimal controller attain good modelling and control performances.

Inverse optimal control (IOC) is a problem of estimating a cost function based on the behaviors of an expert that behaves optimally with respect to the cost function. Although the Hamilton-Jacobi-Bellman (HJB) equation for the value function that evaluates the temporal integral of the cost function provides a necessary condition for the optimality of expert behaviors, the use of the HJB equation alone is insufficient for solving the IOC problem. In this study, we propose a triangle inequality which is useful for estimating the better representation of the value function, along with a new IOC method incorporating the triangle inequality. Through several IOC problems and imitation learning problems of time-dependent control behaviors, we show that our IOC method performs substantially better than an existing IOC method. Showing our IOC method is also applicable to an imitation of expert control of a 2-link manipulator, we demonstrate applicability of our method to real-world problems.

This study utilizes inverse optimal control (IOC) theory to address the issue of output voltage regulation in a boost converter feeding an unknown direct current (DC) load. The proposed approach involves developing a general feedback control law through IOC to ensure asymptotic stability in closed-loop operation, with the added advantage of incorporating an integral gain without compromising stability. Two estimators are introduced to minimize the number of sensors required for implementing the IOC controller with integral action. The first estimator, based on the immersion and invariance (I&I) method, determines the current demand of the DC load by measuring the boost converter’s output voltage. While the second estimator, using the disturbance observer (DO) method, estimates the voltage input value by measuring the inductor’s current flow. Both methods guarantee exponential convergence to the precise value of the estimated variable, irrespective of the initial estimation points. Experimental validation using varying DC loads and estimation techniques confirms the proposed IOC approach’s effectiveness and robustness in regulating voltage for DC loads connected to a boost converter. Furthermore, the proposed controller is compared to the sliding mode control and presents a better performance with a more straightforward design, and the stability in closed-loop ensured.

This paper addresses the adaptive inverse optimal output regulation problem for a class of uncertain nonlinear systems driven by an exosystem. The unknown parameters, internal disturbances, and unmeasured states are contained in the nonlinear system. Firstly, the output regulation problem is decomposed into a feedforward control design problem which can be solved by the internal model based on the output regulation theory, and an adaptive inverse optimal stabilization problem. Then an auxiliary system is designed, and a new state observer related to the auxiliary system is given. By combining adaptive control technology and inverse optimal control method, a novel adaptive output feedback inverse optimal controller is developed to make the output of the system track the reference signal fast. With this control strategy, all the signals of the closed-loop system are uniformly ultimately bounded (UUB), and the newly well-defined cost functional which is connected with the auxiliary system and the controller can be minimized. Finally, a simulation case is put forward to verify the feasibility of the newly raised controller and the state observer.

Inverse optimal control is a widely used technique for solving various optimal problems arising in the controlled system. However, this method becomes inapplicable to optimal problems when the system has disturbances. In this article, we propose a novel anti‐disturbance inverse optimal controller design for a class of high‐dimensional chain structure systems with any disturbances, matched, or mismatched. First, a disturbance observer is employed to get the estimates of the disturbances in the system. Then using backstepping approach, the disturbance estimation is incorporated in the virtual control laws, and consequently a control Lyapunov function (CLF) is obtained. Finally, a composite controller is designed by developing an inverse optimal control method using the obtained CLF function. We show the stability analysis of the anti‐disturbance controller with rigorous proofs, which minimizes an optimal index while the output converges. Moreover, simulation study and analysis for real application to DC–DC buck converters reveal that the proposed composite controller achieves good performance and stabilizes the system with disturbances. [ABSTRACT FROM AUTHOR]

Inverse optimal control is a method for recovering the cost function used in an optimal control problem in expert demonstrations. Most studies on inverse optimal control have focused on building the unknown cost function through the linear combination of given features with unknown cost weights, which are generally considered to be constant. However, in many real-world applications, the cost weights may vary over time. In this study, we propose an adaptive online inverse optimal control approach based on a neural-network approximation to address the challenge of recovering time-varying cost weights. We conduct a well-posedness analysis of the problem and suggest a condition for the adaptive goal, under which the weights of the neural network generated to achieve this adaptive goal are unique to the corresponding inverse optimal control problem. Furthermore, we propose an updating law for the weights of the neural network to ensure the stability of the convergence of the solutions. Finally, simulation results for an example linear system are presented to demonstrate the effectiveness of the proposed strategy. The proposed method is applicable to a wide range of problems requiring real-time inverse optimal control calculations.

This paper presents the development of a neural inverse optimal control (NIOC) for a regenerative braking system installed in electric vehicles (EVs), which is composed of a main energy system (MES) including a storage system and an auxiliary energy system (AES). This last one is composed of a supercapacitor and a buck–boost converter. The AES aims to recover the energy generated during braking that the MES is incapable of saving and using later during the speed increase. To build up the NIOC, a neural identifier has been trained with an extended Kalman filter (EKF) to estimate the real dynamics of the buck–boost converter. The NIOC is implemented to regulate the voltage and current dynamics in the AES. For testing the drive system of the EV, a DC motor is considered where the speed is controlled using a PID controller to regulate the tracking source in the regenerative braking. Simulation results illustrate the efficiency of the proposed control scheme to track time-varying references of the AES voltage and current dynamics measured at the buck–boost converter and to guarantee the charging and discharging operation modes of the supercapacitor. In addition, it is demonstrated that the proposed control scheme enhances the EV storage system's efficacy and performance when the regenerative braking system is working. Furthermore, the mean squared error is calculated to prove and compare the proposed control scheme with the mean squared error for a PID controller. [ABSTRACT FROM AUTHOR]

This article proposes robust inverse $Q$ -learning algorithms for a learner to mimic an expert’s states and control inputs in the imitation learning problem. These two agents have different adversarial disturbances. To do the imitation, the learner must reconstruct the unknown expert cost function. The learner only observes the expert’s control inputs and uses inverse $Q$ -learning algorithms to reconstruct the unknown expert cost function. The inverse $Q$ -learning algorithms are robust in that they are independent of the system model and allow for the different cost function parameters and disturbances between two agents. We first propose an offline inverse $Q$ -learning algorithm which consists of two iterative learning loops: 1) an inner $Q$ -learning iteration loop and 2) an outer iteration loop based on inverse optimal control. Then, based on this offline algorithm, we further develop an online inverse $Q$ -learning algorithm such that the learner mimics the expert behaviors online with the real-time observation of the expert control inputs. This online computational method has four functional approximators: a critic approximator, two actor approximators, and a state-reward neural network (NN). It simultaneously approximates the parameters of $Q$ -function and the learner state reward online. Convergence and stability proofs are rigorously studied to guarantee the algorithm performance. [ABSTRACT FROM AUTHOR]

This paper proposes an impulsive control scheme for a complex network that helps reduce the spread of two epidemic diseases: influenza type A and COVID-19. Both are respiratory infections; thus, they have a similar form of transmission, and it is possible to use the same control scheme in both study cases. The objective of this work is to use neural impulsive inverse optimal pinning control for complex networks to reduce the effects of propagation. The dynamic model is considered unknown, for which we design a neural identifier that, through training using the extended Kalman filter algorithm, provides the appropriate nonlinear model for this complex network. The dynamics of the network nodes are represented by the Susceptible-Infected-Removed (SIR) compartmental model in their discrete form. The results of the simulations are presented and addressed, applying the same control scheme but with different parameter values for each case study. [ABSTRACT FROM AUTHOR]

The paper addresses the inverse problem in the case of linear-quadratic discrete-time dynamic non-cooperative games. We consider a game with some unknown cost function parameters, referred to as the observed game, that has a set of known feedback laws constituting a Nash equilibrium. The inverse problem is to find values of the cost function parameters that together with the observed game dynamics form a new game, equivalent to the observed one in the sense that it has the same Nash equilibrium. We present a model-based algorithm to solve this problem. We prove the convergence of the algorithm and show that the given set of feedback laws is a Nash equilibrium for the designed game. We also demonstrate how to generate new games with the required properties without repeatedly running the complete algorithm. Moreover, the model-based algorithm is extended to a model-free version that operates without requiring the knowledge of the system matrices, but relies on the ability to collect sufficient data. Simulation results validate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

An efficient inverse optimal control method named Adaptive Reference IOC is introduced to study natural walking with musculoskeletal models. Adaptive Reference IOC utilizes efficient inner-loop direct collocation for optimal trajectory prediction along with a gradient-based weight update inspired by structured classification in the outer-loop to achieve about 7 times faster convergence than existing derivative-free methods while maintaining similar outcomes in terms of gait trajectory matching. The proposed method adequately reconstructed the reference data when applied to experimental walking data from ten participants walking at various speeds and stride lengths. The proposed framework can facilitate efficient personalized cost function optimization for specific walking tasks, and provide guidance to personalized reference trajectory design for assistive robotic systems such as lower-limb exoskeletons.

In this paper, we present a Model-Free Stochastic Inverse Optimal Control (IOC) algorithm for the discrete-time infinite-horizon stochastic linear quadratic regulator (LQR). Our proposed algorithm exploits the richness of the available system trajectories to recover the control gain $K$ and cost function parameters $(Q,R)$ in a low (space, sample, and computational) complexity manner. By leveraging insights on the stochastic LQR, we guarantee well-posedness of the Model-Free Stochastic IOC LQR via satisfaction of the Certainty Equivalence optimality conditions. The exact solution of the control gain $K$ is recovered via a deterministic, low complexity Least Squares approach. Using $K$ , we solve a completely model-free non-iterative SemiDefinite Programming (SDP) problem to obtain a unique (up to a scalar ambiguity) $(Q,R)$ , in which optimality and feasibility are jointly ensured. Via derivation of the sample complexity bounds, we show that the non-asymptotic performance of the Model-Free Stochastic IOC LQR can be characterized by the signal-to-noise (SNR) ratio of the finite set of system state and input signals. We present a model-based version of the algorithm for the special case where $(A,B)$ is available, and we, further, provide the extension to the Stochastic Model-Free IOC linear quadratic tracking (LQT) case.

In this paper, the utilization of inverse-optimality-based prescribed-time explicit reference governor is investigated for missile intercepting against unknown maneuvering targets under performance and control input constraints. With an arctangent-based disturbance observer equipped for disturbance elimination, incorporating the inverse optimality approach into the missile interception guarantees the minimization of a performance index. In the framework of prescribed-time explicit reference governor, the control constraint is translated into a restriction of time-varying invariant set, and it follows the prescribed-time regulation of the applied reference along with the restriction satisfaction. The combined prescribed-time explicit reference governor approach could be transformed into a linear matrix inequality optimization problem, and its online solution over a receding horizon gives a Lyapunov function value for reference regulation and then control decisions in the continuous time. Simulation studies are performed to illustrate the performance of the proposed guidance control law. • Arctangent-based disturbance observer compensates lumped external disturbances for better performance. • Inverse optimality guidance approach guarantees the minimization of a performance index. • Prescribed-time ERG generates a time-varying invariant set for constraint satisfaction. • The online solution of LMI gives a Lyapunov function value for reference regulation. [ABSTRACT FROM AUTHOR]

Most existing methods on optimal finite-time control are restricted to a complex design and learning procedure, and only practical finite-time stable is ensured, which greatly limits the desirable performance of optimal and finite-time control. To solve the problem, an adaptive fuzzy fixed-time inverse approach is first proposed in this article, which achieves the optimized performance without recourse to Hamilton–Jacobi–Bellman equations and improves practical finite/fixed-time stable to fixed-time stable. Technically, to overcome the inverse optimal design difficulty of a nonlinear fixed-time controller, a series of singularity-avoidance functions and a Sontag-type function are incorporated to design a specified form of auxiliary controller, based on which an inverse optimal fixed-time controller is designed. Then, by introducing a two-Lyapunov functions method, it is proved that inverse optimal stabilization is ensured and the tracking error goes to a prescribed interval asymptotically within a fixed-time. Effectiveness of the proposed methods are illustrated by two examples. [ABSTRACT FROM AUTHOR]

This paper studies the inverse optimal control using Legendre-Fenchel (in short, LF) translation method for regime-switching jump diffusions. Our approach is to first design inverse pre-optimal stabilization controllers and then obtain inverse optimal stabilizers, which avoids solving a Hamilton-Jacobi-Bellman equation. Finally, an application to stochastic Hamiltonian systems with Markov regime-switching is studied in detail for illustration. [ABSTRACT FROM AUTHOR]

This article addresses the problem regarding power regulation in classical DC-DC second-order converters by means of a nonlinear control technique based on inverse optimal control theory. There are few papers that describe inverse optimal control for DC-DC converters in the literature. Therefore, this study constitutes a contribution to the state of the art on nonlinear control techniques for DC-DC converters. In this vein, the main objective of this research was to implement inverse optimal control theory with integral action to the typical DC-DC conversion topologies for power regulation, regardless of the load variations and the application. The converter topologies analyzed were: (i) Buck; (ii) Boost; (iii) Buck-Boost; and (iv) Non-Inverting Buck-Boost. A dynamical model was proposed as a function of the state variable error, which helped to demonstrate that the inverse optimal control law with proportional-integral action implemented in the different converters ensures stability in each closed-loop operation via Lyapunov’s theorem. Numerical validations were carried out by means of simulations in the PSIM software, comparing the established control law, the passivity-based PI control law, and an open-loop control. As a conclusion, it was possible to determine that the proposed model is easier to implement and has a better dynamical behavior than the PI-PBC, ensuring asymptotic stability from the closed-loop control design.

In this paper, we propose an inverse optimal composite control (IOCC) method to solve the optimization problem for a class of high-dimensional nonlinear strict-feedback systems with disturbances. Initially, we give these systems an inverse optimal control framework that avoids solving Hamilton–Jacobi-Bellman equations. Then, a nonlinear disturbance observer is designed to estimate the disturbances in the systems. We incorporate these disturbance estimates into the virtual control law design through a backstepping method that gives us a control Lyapunov function. In the end, this control Lyapunov function is utilized to obtain a composite controller that achieves optimality and disturbance rejection. We provide rigorous proofs for the convergence of the proposed composite controller. Simulation studies and comparative results from a real-life application to single-link robots show that the proposed composite controller achieves more robustness and effectiveness than the popular control methods in high-dimensional nonlinear systems. [ABSTRACT FROM AUTHOR]

Learning from demonstration, or imitation learning, is the process of learning to act in an environment from examples provided by a teacher. Inverse reinforcement learning (IRL) is a specific form of learning from demonstration that attempts to estimate the reward function of a Markov decision process from examples provided by the teacher. The reward function is often considered the most succinct description of a task. In simple applications, the reward function may be known or easily derived from properties of the system and hard coded into the learning process. However, in complex applications, this may not be possible, and it may be easier to learn the reward function by observing the actions of the teacher. This paper provides a comprehensive survey of the literature on IRL. This survey outlines the differences between IRL and two similar methods - apprenticeship learning and inverse optimal control. Further, this survey organizes the IRL literature based on the principal method, describes applications of IRL algorithms, and provides areas of future research. [ABSTRACT FROM AUTHOR]

An efficient inverse optimal control method named Adaptive Reference IOC is introduced to study natural walking with musculoskeletal models. Adaptive Reference IOC utilizes efficient inner-loop direct collocation for optimal trajectory prediction along with a gradient-based weight update inspired by structured classification in the outer-loop to achieve about 7 times faster convergence than existing derivative-free methods while maintaining similar outcomes in terms of gait trajectory matching. The proposed method adequately reconstructed the reference data when applied to experimental walking data from ten participants walking at various speeds and stride lengths. The proposed framework can facilitate efficient personalized cost function optimization for specific walking tasks, and provide guidance to personalized reference trajectory design for assistive robotic systems such as lower-limb exoskeletons. [ABSTRACT FROM AUTHOR]

Optimized performance obtained from existing adaptive fuzzy optimal control methods comes at the cost of a intricate design procedure and a heavy computation of online parameter learning, and it is an under-explored problem on how to remove such a restriction. In this article, we tackle this problem and ensure the optimized performance using only one adaptive parameter. To this end, a direct adaptive fuzzy inverse approach is first proposed to design a switching-type inverse optimal controller and a one-parameter learning mechanism. It is proved that the proposed approach ensures the input-to-state stability of the control system and besides, the inverse optimality in regard to a meaningful cost functional is achieved. Illustrative examples verify the approach developed. [ABSTRACT FROM AUTHOR]

In this article, an event-triggered adaptive neural network (NN) output-feedback inverse optimal control issue is investigated for the steer-by-wire vehicle (SBWV) systems. Firstly, NNs are utilized to approximate the unknown nonlinear dynamics and the auxiliary system of SBWV systems is established. Then, a NN state observer is constructed to estimate the unmeasured states. To obtain better tracking performance, the prescribed performance technique is introduced to constrain the tracking error. An event-triggered mechanism (ETM) is established to decrease the numbers of controller execution times. Subsequently, an event-triggered adaptive NN inverse optimal output-feedback control algorithm is proposed by employing the backstepping control theory. It is proved that the developed control method can not only ensure the stability of the SBWV systems, but also guarantee the tracking error does not exceed the prescribed performance bound and converges to a small neighborhood of zero. Finally, simulation results are given to verify the validity of the proposed control method. [ABSTRACT FROM AUTHOR]

This article focuses on the issue of addressing an adaptive neural network (NN) inverse optimal containment control for nonlinear multiagent systems (MASs), which are subject to immeasurable states and quantized input signals simultaneously. To tackle this problem, we utilize a NN to model unknown agents and design a NN observer to estimate the immeasurable states. Additionally, we decompose the hysteretic quantized input into two bounded nonlinear functions. By employing the adaptive backstepping approach and inverse optimal principle, we formulate an adaptive NN inverse optimal containment control method. The developed inverse optimal containment control scheme guarantees that the controlled system is input-to-state stabilizable (ISS). Finally, we validate the effectiveness of our proposed control scheme through simulation results. [ABSTRACT FROM AUTHOR]

The Inverse Optimal Control (IOC) problem is a structured system identification problem that aims to identify the underlying objective function based on observed optimal trajectories. This provides a data-driven way to model experts' behavior. In this paper, we consider the case of discrete-time finite-horizon linear–quadratic problems where: the quadratic cost term in the objective is not necessarily positive semi-definite; the planning horizon is a random variable; we have both process noise and observation noise; the dynamics can have a drift term; and where we can have a linear cost term in the objective. In this setting, we first formulate the necessary and sufficient conditions for when the forward optimal control problem is solvable. Next, we show that the corresponding IOC problem is identifiable. Using the conditions for existence of an optimum of the forward problem, we then formulate an estimator for the parameters in the objective function of the forward problem as the globally optimal solution to a convex optimization problem, and prove that the estimator is statistical consistent. Finally, the performance of the algorithm is demonstrated on two numerical examples. [ABSTRACT FROM AUTHOR]

A novel control strategy for secondary restoration of an islanded microgrid is proposed, focusing on restoring the frequency and voltage magnitude of an inverter-based distributed generator. A neural inverse optimal controller is integrated into the secondary control layer with a higher-order neural network trained using an extended Kalman filter (EKF). A practical and effective design strategy is provided. Unlike traditional approaches that rely on accurate mathematical models, the combination of inverse optimal control and neural networks does not require an accurate model and is more relevant to real-world engineering scenarios. To enhance the secondary control, the EKF optimization parameters are used in conjunction with the inverse optimal control to achieve more accurate and effective repair results. The synergistic effect improves control performance and ensures superior secondary recovery. Real-time validation is performed through rigorous simulations on the StarSim hardware-in-the-loop experimental platform. • Practical controller design for more real-world engineering: The approach combines inverse optimal control with neural networks, eliminating the need for exact models and providing a more practical and realistic controller design for the complexity of engineering applications. • Enhanced secondary control precision: The integration of EKF optimization with inverse optimal control results in a more accurate and effective secondary restoration. • Real-time validation through hardware-in-loop simulation: To validate the proposed control strategy in real-world scenarios, rigorous simulations are conducted on the StarSim Hardware-in-loop experimental platform. [ABSTRACT FROM AUTHOR]

• We propose a new framework to solve asset allocation/consumption under risk aversion. • This new model relies on the indirect utility as the primitive of the framework. • The indirect utility function is a function of wealth and is then easily recovered from investors' trading positions. • We show the efficiency of our approach through a strategy in the S&P500 market. Articles about asset allocation rely on the direct utility as a primitive to model the risk appetite of investors and to derive optimal asset allocation and consumption. In a simple setting, we show that the same problem can be solved where the indirect utility function is used as a primitive. Our approach offers various advantages. The indirect utility function measures the satisfaction at optimum and perfectly describes the risk appetite of investors. It is a function of wealth whereas the direct utility function depends on consumption. [ABSTRACT FROM AUTHOR]