Computation Of Control Law Research Articles

Computation of feedback control laws based on switched tracking of demonstrations

A common approach in robotics is to learn tasks by generalizing from special cases given by a so-called demonstrator. In this paper, we apply this paradigm and present an algorithm that uses a demonstrator (typically given by a trajectory optimizer) to automatically synthesize feedback controllers for steering a system described by ordinary differential equations into a goal set. The resulting feedback control law switches between the demonstrations that it uses as reference trajectories. In comparison to the direct use of trajectory optimization as a control law, for example, in the form of model predictive control, this allows for a much simpler and more efficient implementation of the controller. The synthesis algorithm comes with rigorous convergence and optimality results, and computational experiments confirm its efficiency.

Private outsourced model predictive control via secure multi-party computation

Protecting data privacy is essential in developing practical cloud-based control systems to benefit from remote and distributed computation while avoiding the risks of disclosing sensitive information to potentially untrusted parties. This paper proposes a privacy-preserving framework to outsource the computation of model predictive control law to several untrusted cloud-based servers. A secret sharing scheme is employed to maintain the privacy of the system’s data in all the stages of the control loop in a secure multi-party computation environment. In this regard, a privacy-preserving algorithm is derived to securely implement a projected gradient method to solve the underlying optimization problem, without revealing private data to external eavesdroppers and curious cloud-based servers. The proposed method is solely based on secret sharing, and all computations can be performed securely by cloud servers without the need to designate target nodes or engage the system’s actuator in computing the intermediate steps. Therefore, the proposed method is less computationally demanding than the existing results based on homomorphic encryption and is applicable to systems with limited computing resources. Information-theoretic privacy assessments based on mutual information measures are provided. The efficacy of the proposed method is investigated on the cruise control problem of a freight train system.

Adaptive control for shape memory alloy actuated systems with applications to human-robot interaction.

Shape memory alloy (SMA) actuators are attractive options for robotic applications due to their salient features. So far, achieving precise control of SMA actuators and applying them to human-robot interaction scenarios remains a challenge. This paper proposes a novel approach to deal with the control problem of a SMA actuator. Departing from conventional mechanism models, we attempt to describe this nonlinear plant using a gray-box model, in which only the input current and the output displacement are measured. The control scheme consists of the model parameters updating and the control law calculation. The adaptation algorithm is founded on the multi-innovation concept and incorporates a dead-zone weighted factor, aiming to concurrently reduce computational complexities and enhance robustness properties. The control law is based on a PI controller, the gains of which are designed by the pole assignment technique. Theoretical analysis proves that the closed-loop performance can be ensured under mild conditions. The experiments are first conducted through the Beckhoff controller. The comparative results suggest that the proposed adaptive PI control strategy exhibits broad applicability, particularly under load variations. Subsequently, the SMA actuator is designed and incorporated into the hand rehabilitation robot. System position tracking experiments and passive rehabilitation training experiments for various gestures are then conducted. The experimental outcomes demonstrate that the hand rehabilitation robot, utilizing the SMA actuator, achieves higher position tracking accuracy and a more stable system under the adaptive control strategy proposed in this paper. Simultaneously, it successfully accommodates hand rehabilitation movements for multiple gestures. The adaptive controller proposed in this paper takes into account both the computational complexity of the model and the accuracy of the control results, Experimental results not only demonstrate the practicality and reliability of the controller but also attest to its potential application in human-machine interaction within the field of neural rehabilitation.

Overcoming backstepping limitations via a novel MIMO non-affine-in-control convex optimization technique

Limitations of the standard backstepping control technique are overcome in this paper by yielding global conditions for regional ones; specifically, flexible cascade arrangements that do not require the system to be put in a pure- or strict-feedback form to ensure controllability beforehand, handling of nonlinear MIMO blocks without invertible input distribution matrices, calculation of virtual and real control laws regardless of the non-affine-in-control nature of subsystems, and systematic numerical synthesis of Lyapunov-based control laws at each step of the cascade connection via linear matrix inequalities. All these benefits derive from exploiting exact convex rewriting of nonlinear terms, splitting available and non-available signals for control implementation, and applying the direct Lyapunov method to cast conditions as a convex optimization problem. Examples of academic and practical interest illustrate the advantages of the novel methodology over former approaches.

Visual path following with obstacle avoidance for quadcopters in indoor environments

In this paper, we propose a hierarchical visual servo control scheme for following visual paths with quadcopters in indoor environments. The control scheme is able to deal with three tasks simultaneously, considering as order of hierarchy: first, collision avoidance task, second visibility task (keep point features in the camera’s field of view), and finally, visual servoing task. The strategy allows a commitment of active tasks (also the smooth deactivation of tasks) for avoiding conflicts between them. The proposed scheme uses a monocular RGB front-facing camera as single sensor, i.e., only 2D information is required for the control law computation. That information is used for online reactive visual path following, i.e., no 3D reconstruction of the environment is required, and no path or motion planning for obstacle avoidance is performed while the robot follows the visual path. The effectiveness of the proposed control scheme is supported by a stability analysis and experiments with a low-cost commercial quadcopter in scenarios with static obstacles.

Trajectory planning and control of convection reaction models with storage effects

Distributed parameter systems consisting of several convection-reaction equations, which are distributed coupled with a reaction equation are considered. An alternative model description for this class of systems is obtained using the method of characteristics. The alternative description is constituted by a single partial differential equation of first order with respect to time. The proposed reformulation of the model allows for the efficient simulation of the system and for the straightforward calculation of inversion-based open-loop control laws. The stability of the original and the inverse models are discussed. The proposed method is illustrated by means of an example.

Long-term deorbiting control for an electrodynamic tether system exploiting periodic solutions

This paper focuses on the nonlinear dynamics and control problem of deorbiting an electrodynamic tethered satellite system in an inclined elliptical orbit. Considering the perturbing Lorenz forces, a set of modified equinoctial elements is employed to describe the slow-varying orbital dynamics. In addition, the fast-varying attitude dynamics of the system is incorporated into dynamic modeling by adopting an assumption of a dumbbell model. To circumvent the difficulties in computation of a real-time optimal control law for a long-term deorbiting process, a compound control scheme is proposed. A time-scale separation method is adopted to facilitate the controller design. In the scheme, a nonlinear optimal control law accounting for system constraints and nonlinear dynamics is first proposed to find an initial nominal periodic orbit without considering the variations of orbital elements. Subsequently, a closed-loop feedback control law based on energy rate is presented to track the periodic solutions for several orbits by considering the overall dynamics. Notably, the periodic solution will be re-computed after each tracking procedure to account for the slow variation in orbital elements. Comparative studies are presented to demonstrate the advantages of the proposed control law in reducing computational costs.

Platoon-actuated variable area mainstream traffic control for bottleneck decongestion

In this paper a platoon-actuated mainstream traffic control is proposed to decongest bottlenecks due to recurrent and nonrecurrent events. Indeed, differently from traditional mainstream control strategies, i.e., control strategies applied with fixed actuators, platoon-actuated control can be applied at any location on the freeway. In this work, the control actions to be communicated to the platoons, i.e., speed and configuration, are defined by means of a predictive control law based on traffic and platoon state detected in an area identified immediately upstream of the bottleneck. The main peculiarity of this scheme is that the size of the controlled area is dynamically adjusted based on the predicted congestion at the bottleneck. This approach keeps the control law computation burden low, while not sacrificing much control performance. Specifically, the number of platoons to be controlled and the time at which the platoons begin to be controlled depend on the size of the controlled area. Simulation results reported in the paper show the effectiveness of the proposed scheme, eliminating from 60% to 80% of the delay incurred from congestion compared with the uncontrolled case, depending on the level of traffic.

On the Existence and Computation of Minimum Attention Optimal Control Laws

One means of capturing the cost of control implementation of a general nonlinear control system is via Brockett's minimum attention criterion, defined as a multidimensional integral of the rate of change of the control with respect to state and time. Although shown to be important in human motor control and robotics applications, a practical difficulty with this criterion is that the existence of solutions is not always assured; even when they exist, obtaining local solutions numerically is difficult. In this paper we prove that, for the class of controls consisting of the sum of a time-varying feedforward term and a time-varying feedback term linear in the state, existence of a suboptimal solution can be guaranteed. We also derive a provably convergent gradient descent algorithm for obtaining a local solution, by appealing to the Liouville equation representation of a nonlinear control system and adapting iterative methods originally developed for boundary flow control. Our methodology is illustrated with a two degree-of-freedom planar robot example.

Computation of Control Law for State Transfer Problem in Efficient Way for a Single Input

This article proposes a modified way to compute open loop control for the state transfer problem (STP) for a linear time-invariant system. Solving STP analytically is a cumbersome task. This is mainly due to tedious computations of state-transition matrix and controllability Gramian matrix. The proposed modified method enables to find control law easily and with less computations. This approach is applicable even for a third-order or higher order system with single input case analytically and without use of computer. Moreover, the proposed approach minimizes the use of calculator and thereby reduces the computational rounding-off errors. Finally, it is shown that for some special case with knowledge of mode vector, the STP can be solved very quickly without even calculating the state-transition matrix and controllability Gramian matrix. Furthermore, theoretical as well as experimental evaluation of control law is provided. Experimental results are used to validate the proposed method.

Region coverage control for multiple stratospheric airships with combined self-/event-triggered mechanism

The region coverage control problem of multiple stratospheric airships system is firstly addressed in this paper. Towards it, we propose a two-layer control framework with the artificial potential field (APF)-based region coverage control law and the adaptive tracking control law. The APF-based region coverage control law ensures the coverage task is achieved until every single stratospheric airship ends up performing station keeping where near the respective global minimum point, in which an innovative solution to the local minimum problem is put forward. The adaptive tracking control law is designed to realize motion control using tracking the desired velocity and angular velocity given by coverage control law, with the consideration of several practical control problems as unknown individual differences and external disturbances. To save resources, the combined self-/event-triggered mechanism designed therein significantly reduces the times of state information transmission and control law calculation. The effectiveness of the proposed control framework is verified through simulations.

Event-triggered output feedback containment control for a class of stochastic nonlinear multi-agent systems

An output feedback-based containment control strategy is proposed with an event-triggered mechanism for a class of stochastic nonlinear multi-agent systems (MASs). For unavailable internal states of individual agent, a state observer is constructed for their estimations. The dynamic surface control (DSC) technology is employed to improve traditional backstepping, where a first-order filter is introduced for derivation calculation of virtual control laws. For the purpose of reducing communication resources, a fixed threshold-based triggered strategy is presented to reduce data transmission bits over communication channels. It is proven that all signals in the closed-loop system are bounded in probability and the containment control is achieved. Finally, the effectiveness of the proposed control strategy is verified via two examples.

On-ramp merging strategy for connected and automated vehicles based on complete information static game

Improper handling of vehicle on-ramp merging may hinder traffic flow and contribute to lower fuel economy, while also increasing the risk of collisions. Cooperative control for connected and automated vehicles (CAVs) has the potential to significantly reduce negative environmental impact while also improve driving safety and traffic efficiency. Therefore, in this paper, we focus on the scenario of CAVs on-ramp merging and propose a centralized control method. Merging sequence (MS) allocation and motion planning are two key issues in this process. To deal with these problems, we first propose an MS allocation method based on a complete information static game whereby the mixed-strategy Nash equilibrium is calculated for an individual vehicle to select its strategy. The on-ramp merging problem is then formulated as a bi-objective (total fuel consumption and total travel time) optimization problem, to which optimal control based on Pontryagin's minimum principle (PMP) is applied to solve the motion planning issue. To determine the proper parameters in the bi-objective optimization problem, a varying-scale grid search method is proposed to explore possible solutions at different scales. In this method, an improved quicksort algorithm is designed to search for the Pareto front, and the (approximately) unbiased Pareto solution for the bi-objective optimization problem is finally determined as the optimal solution. The proposed on-ramp merging strategy is validated via numerical simulation, and comparison with other strategies demonstrates its effectiveness in terms of fuel economy and traffic efficiency. • MS allocation is modeled as a two-player game, where Pontryagin's minimum principle is used for control law calculation. • Illustrating in detail mixed-strategy Nash equilibrium of the game for MS allocation. • Proposing a varying-scale grid search algorithm to search for candidated parameters in the cost function.

Nonlinear state-feedback design for vehicle lateral control using sum-of-squares programming

ABSTRACT This work addresses the lateral stabilisation problem of four-wheels ground vehicles. The objective is to estimate the largest state-space region such that the closed-loop vehicle lateral stability can be guaranteed. Sum-of-squares (SOS) programming technique is applied to find these maximum invariant sets while accounting for steering and yaw moment input saturations. The algorithm allows the region of attraction (RoA) to be approximated by a level set of a Lyapunov function (LF) and the computation of polynomial state feedback control laws. The method is applied for both straight-line motion and cornering manoeuver. Finally, a Monte-Carlo analysis is presented to show that the proposed SOS-based methodology can be used as a valid analysis and design tool considering a real vehicle application.

Improved Q-Learning Method for Linear Discrete-Time Systems

In this paper, the Q-learning method for quadratic optimal control problem of discrete-time linear systems is reconsidered. The theoretical results prove that the quadratic optimal controller cannot be solved directly due to the linear correlation of the data sets. The following corollaries have been made: (1) The correlation of data is the key factor in the success for the calculation of quadratic optimal control laws by Q-learning method; (2) The control laws for linear systems cannot be derived directly by the existing Q-learning method; (3) For nonlinear systems, there are some doubts about the data independence of current method. Therefore, it is necessary to discuss the probability of the controllers established by the existing Q-learning method. To solve this problem, based on the ridge regression, an improved model-free Q-learning quadratic optimal control method for discrete-time linear systems is proposed in this paper. Therefore, the computation process can be implemented correctly, and the effective controller can be solved. The simulation results show that the proposed method can not only overcome the problem caused by the data correlation, but also derive proper control laws for discrete-time linear systems.

A guidance approach to satellite formation reconfiguration based on convex optimization and genetic algorithms

This paper presents a new approach for autonomous reconfiguration of distributed space systems, which ensures safe guidance of spacecraft formations towards the desired patterns while optimizing the total propellant consumption. The orbital transfer is reduced to the form of a convex optimization problem to guarantee rapid computation of control laws. Hence, tasks are iteratively assigned to the component platforms to detect the best reconfiguration strategy. The path-planning is entrusted to a reference satellite of the cluster, that coordinates the remaining ones by means of a procedure based on genetic algorithms. Two methods are proposed, depending on the organizational architecture of the spacecraft formation. In the first one, the maneuver is completely planned by the reference satellite, that determines final tasks and control actions for the whole cluster. As an alternative to such a fully-centralized approach, a distributed version of the algorithm is proposed: tasks are sorted by the reference satellite and transfer orbits are computed by exploiting the computational resources of the whole cluster. Whatever the considered framework, both the planners ensure a safe transition of the formation towards the target geometry. Simulation results show that, when relative distances are of the order of hundreds of meters, a mean delta-v per satellite of the order of 0.1 m/s is required to reconfigure LEO clusters within one orbital period.

Sub-optimal Control Design for Second Order Non-linear Systems using Krotov Sufficient Conditions

This article considers the problem of sub-optimal control design problem for second order non-linear systems. Traditionally, the computation of optimal control law(s) for non-linear systems is usually done using the iterative methods based on the standard tools of optimal control theory which viz. Calculus of Variations (CoV), Hamilton-Jacobi-Bellman equation, Pontryagin’s principle, etc. This work utilizes the rather less explored technique, namely the Krotov framework to obtain the non-iterative solutions. These conditions are derived by transforming the optimal control problem into another equivalent optimization problem. This translation is done via an ad-hoc selection of the so-called Krotov function. In this article, the Krotov function is chosen such that the equivalent optimization problem can be solved non-iteratively to obtain sub-optimal control laws for the original optimal control problem. The proposed methodology is demonstrated by a numerical example.

Modified-transformation-based networked controller for offshore platforms under multiple outloads

In the paper, we study the problem of vibration control for offshore platform in nonideal network environment under wave and current forces based on the modified transformation. We consider the wave and current synchronously and give a dynamical system for the outside loads. The problem of time delay, packet dropouts and disordering due to nonideal network are taken into account. In the networked control model, two buffers output the received packets according to time stamps and upper bound of time delay. Based on a transformation, we reduce the time delay system into an equivalent delay-free system. Taking the nonideal network communication conditions into account, we design a modified transformation based on the past time data, wave and current loads, and received packets through network at current time. The networked controller is presented to depress the vibration of structure in nonideal network communication environment based on the modified transformation. An algorithm is given to simplify the computation of control law by recurrence. The system stability under presented networked controller is analyzed based on Lyapunov functional. Through the simulation results and comparison with other networked controllers, we can see that the presented controller can reduce the oscillation of offshore platform effectively.

Performance and energy aware robust specification of control execution patterns under dropped samples

Embedded control systems are prevalent in a multitude of domains such as automotive, avionics, industrial control etc. For such systems, robustness against non-idealities of the compute platform created by situations such as hardware level transient faults (memory errors, sensor reading errors), network packet drops, late arrival of messages etc., is needed to be ensured at the design level. In traditional regular periodic execution of control loops, such guarantees are obtained by oversampling the plant, which requires extra rounds of sensing, control law computation, and actuation. One possible measure for reducing such over-provisioning of computing and communication resources is allowing occasional drops in the execution leading to better resource management as well as energy efficiency. This work showcases a methodology for deriving window-based bounds on possible drops in control loop executions while assuring formal performance guarantees even in the presence of platform-level non-idealities. Derivation of such relaxation bounds in terms of control loop executions help in deciding energy efficient scheduling solutions for low-power resource-constrained embedded control platforms while retaining control performance. The present work provides a structured methodology for deriving performance-aware control execution patterns given an energy-budget and uncertainty specification of the platform executing a set of embedded control loops.

Robust output feedback controller with high-gain observer for automatic clutch

Abstract Precise and stable position control is critical in automatic clutch system, which is a challenging issue because of its nonlinear characteristics, uncertainties of parameters and disturbances, and lack of all-state sensors. Therefore, a novel robust output feedback control method is proposed in this paper to deal with the nonlinearities, uncertainties and modeling errors. First, an electromechanical dry clutch actuator system is formulated by theoretical analysis combined with experimental data. Then, a robust controller is designed, including the recursive control law calculation and a high-gain observer based on output feedback to estimate the unmeasured states. Next, simulations are carried out to verify the effectiveness of proposed method. Finally, experiments are conducted on a hybrid electric powertrain bench and the results show that the proposed method has a satisfactory performance.