Blockchain Papers

Camilla Fioravanti, Christoforos N. Hadjicostis, Gabriele Oliva

Networked Control Systems (NCS) are pivotal for sectors like industrial automation, autonomous vehicles, and smart grids. However, merging communication networks with control loops brings complexities and security vulnerabilities, necessitating strong protection and authentication measures. This paper introduces an innovative Zero-Knowledge Proof (ZKP) scheme tailored for NCSs, enabling a networked controller to prove its knowledge of the dynamical model and its ability to control a discrete-time linear time-invariant (LTI) system to a sensor, without revealing the model. This verification is done through the controller's capacity to produce suitable control signals in response to the sensor's output demands. The completeness, soundness, and zero-knowledge properties of the proposed approach are demonstrated. The scheme is subsequently extended by considering the presence of delays and output noise. Additionally, a dual scenario where the sensor proves its model knowledge to the controller is explored, enhancing the method's versatility. Effectiveness is shown through numerical simulations and a case study on distributed agreement in multi-agent systems.

Yusheng Wei, Zongli Lin

No abstract is available for this record.

Minseok Kim, Jaehoon Park

—In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method. Keywords—Model predictive control, sampled-data control, linear parameter varying systems, LPV I. INTRODUCTION OBILE robots nowadays move autonomously by recognizing external environment and determining the situation through the remote control. With the development of network communication, implementation employing wireless & wired network is widespread [1]. Though control through network is advantageous in maintenance, installation, flexibility and cost, it has to be carefully designed in reality. It may cause instability and performance degradation without considering network induced delay or data packet losses. Therefore, the design of control scheme should consider with aspects and performances of whole systems. Model predictive control (MPC) scheme is very useful since it provides good tracking performance and the MPC tuning parameters are explicitly related to the key characteristics safety, comfort, and fuel economy. But if the model is not accurate, the control technique does not guarantee the stability and performance [2]. Also, an important issue in the implementation of MPC algorithm is the discretization. A continuous-time model is much more natural and accurate in terms of describing the behavior of a system, Also, in network control systems, choosing proper sampling interval is very important for designing suitable controllers. It is clear that a longer sampling period will lead to lower communication channel occupation, few actuation of the controller, and less signal transmission. Thus, it is very important to consider the stabilizing control design problem under a bigger sampling period [5]. For sampled-data systems, the input delay approach has been widely used [4], which is based on the representation of the sampled-data system as a continuous-time system Fig. 1 Mobile robot in X-Y coordination with a delayed control input. Then, the Lyapunov Krasovskii functional (LKF) method can be used to establish the stability conditions. Recently, based on the input delay approach, the sampled-data control problem of dynamical systems with time-varying delay has been investigated in [3], [4]. In this paper, we consider a continuous-time LPV model to handle mobile robot systems and present a model predictive control method for the systems with sampled-data. To the best of authors' knowledge, there are no approaches considering sampled-data MPC for mobile robots. The presented synthesis condition is formulated by construction of a suitable Lyapunov-Krasovskii's functional and control inputs are obtained by minimizing the upper bound of the cost function satisfying the cost monotonicity. Finally, we demonstrate the effectiveness of the proposed approach via numerical simulation. II. DESCRIPTION OF MOBILE ROBOT The dynamics of mobile robot with a rigid body and wheels can be described as follows [1] , (1) where [x,y,θ] denotes the position and orientation of the center with respect to a global frame, v is the translational velocity, and w is the angular velocity. For the given mobile robot, the reference trajectory is set to , (2) where xr, yr, θr are references in Cartesian coordination, vr is the reference translational velocity, and ωr is the reference angular velocity. Considering local coordinate frame, define From (1)-(3), the error dynamics is obtained as In general, systems represented by nonlinear systems can be transformed into Linear Parameter Varying (LPV) systems X˙ (t) = A(¯v(t),ω¯(t),vr(t))X(t) + BU(t), where A(·) is system matrices containing a time varying parameter vector v¯(t),ω¯(t),vr(t), X = [xe,ye,θe] − [¯xe,y¯e,θ¯e], and U = [v − v,ω¯ − ω¯]. By computing Jacobian matrix, the system matrices are given as . For a given sampling rates, the matrix A(¯v(t),ω¯(t),vr(t)) is subject to a polytope set Ω. (5) where Ω = {A1,A2,...,AL} is the convex hull. In the typical system architecture, control signals are conveyed through network communication. In network environments, the control signals pass through zero-order-hold (ZOH) which generate functions with a sequence of hold times 0 ≤ t0 < t1 < ··· < tk ··· < lim tk = +∞. Taking k→∞ consideration of ZOH, the control input is U(t) = KX(tk), t ∈ [tk,tk+1). (6) where K is the control gain matrix. Without loss of generality, it is assumed that the sampled time interval is bounded by h(t) ≤ hM where h(t) = tk+1 − tk, and hM is the maximum sampled delay. Using sampled signals, the systems are expressed as delayed LPV systems X˙ (t) = AiX(t) + BU(t − h(t)). (7) Lemma 1. [5] For given matrices Λ1,Λ2,Ψ, and a scalar 0 ≤ Lemma 2. [6] For given matrices H,N,R > 0 and a continuously differentiable function x(t) in [a,b] ∈ Rn, the following inequality is ensured. (10) (11) , where is any vector,, and x(s) . −b−a a III. MAIN RESULTS The main purpose of this paper is to design a proper sampled-data model predictive controller. Model Predictive Control is used to approximately obtain optimal trajectories. Therefore, choosing the following performance index is reasonable: (12) where Q, R are coefficients. For the given performance index, if the following condition is satisfied . (13) where · denotes 2-norm, then the upper bound of the performance index can be derived instead of directly minimizing performance index. By integrating (13) from i = 1 to i = ∞, one can notice the upper bound of the performance index is less than the Lyapunov function. Before presenting main results, we employed the following representations for simplicity. The matrices ei = R4n×n for i = 1,2,...,4 are matrices composed of nth zero elements with ith identity matrix. (For example, e1 = [I 0 0 0] and e3 = [0 0 I 0]). . With predefined Lemmas and notations, we present design methodology of model predictive control for delayed LPV systems by deriving a set of linear matrix inequality conditions. Theorem 1. For a given parameter hM and a vector X(tk), if U¯ U¯ there exist positive matrices G, 0,V >¯ 0, Y , Z¯1,Z¯2, satisfying the following LMI conditions, the control input at time instant tk guarantees the performance index (12) with γ . (14) (15) (16) (17) (18) where , with then, the state feedback gains are given as K = Y G−1. Proof. Choosing the following Lyapunov-Krasovskii functional (LKF) for t ∈ [tk,tk+1) yields V (xt) = V1(t) + V2(t) + V3(t) (19) where , Differentiate the LKF From Lemma 2, the following holds (23) where Z1,Z2 are auxiliary variables. Taking into account system dynamics (7), (24) Summing up from (20) to (24) leads to V˙ + XT(t)QX(t) + UT(t)RU(t) ≤ ζ(tk)Σ¯ζ(tk) (25) where Pre-and post-multiplying with a matrix γ1/2 × diag{G,G,G,G}, the followings are satisfied with Lemma 1. , (26) Σ1 + hMΣ3 < 0 (27) time (sec) Fig. 2 error response of the system in Example 1 where U¯ = GUG, V¯ = GV G, Z¯1 = GZ1G, Z¯2 = GZ2G, and K = Y G−1. Using Schur complement, The equations in (25) and (26) are equivalent to those of (16) and (17). For every sampling instance, V2 and V3 vanish. Then, the upper bound of LKF is expressed in terms of V1. XT(tk)GP¯1GX(tk) ≤ γ, (28) where γ denotes the bound of optimal performance index. The effect of input saturation is considered similar to the method in [7]. This ends the proof. IV. NUMERICAL EXAMPLE Example 1 This example considered the dynamical equations of the system represented from error dynamics. X˙ (t) = AiX(t) + BU(t − h(t)) (29) where ⎡ −0 ωr − 0.05 0 ⎤⎦ A1 =ω 0.05 0 vr(t) , 0 0 0 ⎡ 0 ωr + 0.05 0 ⎤ A2 =ω + 0.05 0 vr(t) , 0 0 0 ⎦ ⎡−1 0 ⎤ B = 0 0 . ⎣ 0 −1⎦ The model parameters are calculated with a sampling time 0.1s. The sampling time h(t) is less than 0.1 s. Along the reference trajectory, the input is constrained to −0.1 ≤ u(1) ≤ 0.1 and −0.05 ≤ u(2) ≤ 0.05. The corresponding controller gain matrix is Fig. 2 shows the simulation result which is obtained with the above controller gain, taking Q = I, R = I,α = 0.1. V. CONCLUSION The sampled-data MPC method for mobile robot systems have been investigated by considering constrained polytopic LPV model. Based on the input delay model, sufficient conditions for the sampled-data MPC controller design are obtained by constructing a new Lyapunov functional. The effectiveness of the presented method has been verified by illustrating numerical simulation. REFERENCES W. Lucia, F. Tedesco. "A networked-based receding horizon scheme for constrained LPV systems," European Journal of Control, vol. 25, pp. 69-75, 2015. S. Lee, Ju H. Park, D. Ji, S. Won, "Robust model predictive control for LPV systems using relaxation matrices," IET. Control Theory Appl., vol. 1, no. 6, pp. 1567-1573, 2007. A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality: application to time-delay systems, Automatica, vol. 49, no. 8, pp. 2860-2866, 2013. S. Lee, O. Kwon, Quantised MPC for LPV systems by using new LyapunovKrasovskii functional, IET. Control Theory Appl., vol. 11, no. 3, pp. 439-445, 2017. D. Yue, E. Tian, Y. Zhang, and C. Peng, "Delay-distribution-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay," IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 39, no. 2, pp. 503–516, 2009. C.K. Zhang, Y. He, L. Jiang, W. Lin, M. Wu, "Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix," Applied Mathematics and Computation, vol. 294, no. 1, pp. 102-120, 2017. E. Fridman and M. Dambrine, "Control under quantization, saturation and delay: An LMI approach," Automatica, vol. 45, no. 10, pp. 2258–2

Yusheng Wei, Zongli Lin

In this paper, we propose a delay independent control scheme that regulates to zero the state and the control input of a linear input delayed system whose open loop poles are at the origin or in the open left-half plane. Two main features of our control scheme are its nondistributed nature in the sense that only the current state is used in the feedback and its delay independence in the sense that no knowledge of the delay, neither its exact value nor its upper bound, is required. The main ingredients of our control scheme and the regulation proof include a design of the delay independent truncated predictor feedback law with a time-varying feedback parameter, Lyapunov function based adaptation of the time-varying parameter, a mechanism for switching between two update laws of the time-varying parameter, and the partial differential equation based analysis for delayed systems.

Yusheng Wei, Zongli Lin

In this paper, we propose a delay independent control scheme that regulates to zero the state and the control input of a linear input delayed system whose open loop poles are at the origin. Two main features of our control scheme are its non-distributed nature in the sense that only the current state is used in the feedback, and its delay independence in the sense that no knowledge of the delay is required. The main ingredients of our control scheme and the regulation proof include a design of the delay independent truncated predictor feedback law with a time-varying feedback parameter, a Lyapunov function based adaptation of the time-varying parameter, a mechanism for switching between two update laws of the time-varying parameter, and the partial differential equation based analysis for delayed systems.

Yang Liu, Xiao He, Zidong Wang, Zhou Donghua

In this paper, the fault detection and diagnosis problems are considered for a class of discrete nonlinear systems with decentralized event-triggered measurement transmissions. Each sensor determines, according to certain triggering rules, whether to transmit the present measurement to remote filters based on only locally available information. A set of filters is designed where each filter aims to jointly estimate the system states and a specific possible fault. Upper bounds of the estimation error covariances are obtained in the simultaneous presence of the linearization errors and decentralized event-triggered transmissions, and then the filter gains are calculated to minimize such bounds. The filters are designed in a recursive way and thus the algorithm is applicable for online implementation. When a fault is detected, the filter with the least residual is regarded as the one corresponding to the actual fault and its output can be seen as the states and fault estimation. The effectiveness of the proposed method is illustrated by a simulation example.

Danyal Bustan, Naser Pariz, Seyed Kamal Hosseini Sani

No abstract is available for this record.

Qinglei Hu, Bing Xiao, Michael I. Friswell

This study investigates the robust fault-tolerant attitude control of an orbiting spacecraft with a combination of unknown actuator failure, input saturation and external disturbances. A fault-tolerant control scheme based on variable structure control is developed that is robust to the partial loss of actuator effectiveness, where the actuators experience a reduced actuation but are still active. The results are then extended to the case in which some of the actuators fail completely, although some redundancy in actuation is assumed. In contrast to traditional fault-tolerant control methods, the proposed controller does not require knowledge of the actuator faults and is implemented without explicit fault detection, separation and accommodation processes. Moreover, the designed controller rigorously enforces actuator saturation constraints. The associated stability proof is constructive and develops a candidate Lyapunov function that shows the attitude and the angular velocities converge asymptotically to zero. Simulation studies are used to evaluate the closed-loop performance of the proposed control solution and illustrate its robustness to external disturbances, unknown actuator faults and even input saturation.

Roméo Ortega, Gustavo Sanchez Galindo

A complete proof is given of global convergence to zero of the prediction error and asymptotic optimality for a direct adaptive controller is established based on multistep quadratic cost minimization with a receding horizon philosophy. The only substantial assumptions are that the controller designed when the parameters are known, stabilizes the plant and the exact knowledge of the first N y (N y -optimization horizon) impulse response coefficients of the plant. The technical hurdles for the development of a comprehensive convergence theory of this type of controller are also highlighted.