Delays are ubiquitous in modern hybrid systems, which exhibit both continuous and discrete dynamical behaviors. Induced by signal transmission, conversion, the nature of plants, and so on, delays may appear either in the continuous evolution of a hybrid system such that the evolution depends not only on the present state but also on its execution history, or in the discrete switching between its different control modes. In this paper we come up with a new model of hybrid systems, called \emph{delay hybrid automata}, to capture the dynamics of systems with the aforementioned two kinds of delays. Furthermore, based upon this model we study the robust switching controller synthesis problem such that the controlled delay system is able to satisfy the specified safety properties regardless of perturbations. To the end, a novel method is proposed to synthesize switching controllers based on the computation of differential invariants for continuous evolution and backward reachable sets of discrete jumps with delays. Finally, we implement a prototypical tool of our approach and demonstrate it on some case studies.
Switching control strategies that unite a potentially high-performance but uncertified controller and a stabilizing albeit conservative controller are shown to be able to balance safety with efficiency, but have been less studied under partial observation of state. To address this gap, we propose a switching control strategy for partially observed linear-Gaussian systems with provable performance guarantees. We show that the proposed switching strategy is both safe and efficient, in the sense that: (1) the linear-quadratic cost of the system is always bounded even if the original uncertified c…
In this work, we propose a compositional scheme for the safety controller synthesis of interconnected discrete-time stochastic systems with Markovian switching signals. Our proposed approach is based on a notion of so-called control storage certificates computed for individual subsystems, by leveraging which, one can synthesize state-feedback controllers for interconnected systems to enforce safety specifications over finite time horizons. To do so, we employ a sum-of-squares (SOS) optimization approach to search for multiple storage certificates of each switching subsystem while synthesizing …
In this paper, we study the stability of suboptimal H-infinity controllers for time-delay systems. The optimal H-infinity controller may have finitely or infinitely many unstable poles. A stable suboptimal H-infinity controller design procedure is given for each of these cases. The design methods are illustrated with examples.
Sustained research efforts have been devoted to learning optimal controllers for linear stochastic dynamical systems with unknown parameters, but due to the corruption of noise, learned controllers are usually uncertified in the sense that they may destabilize the system. To address this potential instability, we propose a "plug-and-play" modification to the uncertified controller which falls back to a known stabilizing controller when the norm of the state exceeds a certain threshold. We show that the switching strategy enhances the safety of the uncertified controller by making the linear-qu…
Sustained research efforts have been devoted to learning optimal controllers for linear stochastic dynamical systems with unknown parameters, but due to the corruption of noise, learned controllers are usually uncertified in the sense that they may destabilize the system. To address this potential instability, we propose a "plug-and-play" modification to the uncertified controller which falls back to a known stabilizing controller when the norm of the difference between the uncertified and the fall-back control input exceeds a certain threshold. We show that the switching strategy is both safe…
The skew Toeplitz approach is one of the well developed methods to design H-infinity controllers for infinite dimensional systems. In order to be able to use this method the plant needs to be factorized in some special manner. This paper investigates the largest class of SISO time delay systems for which the special factorizations required by the skew Toeplitz approach can be done. Reliable implementation of the optimal controller is also discussed. It is shown that the finite impulse response (FIR) block structure appears in these controllers not only for plants with I/O delays, but also for …
This paper investigates stable suboptimal H-infinity controllers for a class of single-input single-output time-delay systems. For a given plant and weighting functions, the optimal controller minimizing the mixed sensitivity (and the central suboptimal controller) may be unstable with finitely or infinitely many poles in complex right half-plane. For each of these cases search algorithms are proposed to find stable suboptimal H-infinity controllers. These design methods are illustrated with examples.
This paper presents a new method for dynamic output feedback stabilizing controller design for decomposable systems with switching topology and delay. Our approach consists of two steps. In the first step, we model the decomposable systems with switching topology as equivalent LPV systems with a piecewise constant parameter. In the second step, we design stabilizing output feedbacks for these LPV systems in the presence of a time-varying output delay using a trajectory-based stability analysis approach. We do not impose any constraint on the delay derivative. Finally, we illustrate our approac…
Wind turbines are prone to structural degradation, particularly in offshore locations. Based on the structural health condition of the tower, power de-rating strategies can be used to reduce structural loads at the cost of power losses.This paper introduces a novel closed-loop switching control architecture to constrain the thrust in individual turbines. By taking inspiration from developments in the field of reference governors, an existing demanded power tracking controller is extended by a thrust tracking controller. The latter is activated only when a user-defined constraint on fore-aft th…
Weighted sensitivity minimization is studied within the framework of strongly stabilizing (stable) H-infinity controller design for a class of infinite dimensional systems. This problem has been solved by Ganesh and Pearson, [11], for finite dimensional plants using Nevanlinna-Pick interpolation. We extend their technique to a class of unstable time delay systems. Moreover, we illustrate suboptimal solutions, and their robust implementation.
The approach in Foias et al. (1996) is one of the well-developed methods to design H-infinity controllers for general infinite dimensional systems. This approach is applicable if the plant admits a special coprime inner/outer factorization. We give the largest class of single-input-single-output (SISO) time delay systems for which this factorization is possible and factorize the admissible plants. Based on this factorization, we compute the optimal H-infinity performance and eliminate unstable pole-zero cancellations in the optimal H-infinity controller. We extend the results on the finite imp…
In this paper sensitivity minimization problem is considered for a class of unstable time delay systems. Our goal is to find a stable controller stabilizing the feedback system and giving rise to smallest H-infinity norm for the sensitivity function. This problem has been solved by Ganesh and Pearson (1986) for finite dimensional plants using Nevanlinna-Pick interpolation. We extend their technique to include possibly unstable time delay systems. Moreover, we illustrate suboptimal solutions, and their robust implementation.
We design fixed-order strong H-infinity controllers for general time-delay systems. The designer chooses the controller order and may introduce constant time-delays in the controller. We represent the closed-loop system of the plant and the controller as delay differential algebraic equations (DDAEs). This representation deals with any interconnection of systems with time-delays without any elimination techniques. We present a numerical algorithm to compute the strong H-infinity norm for DDAEs which is robust to arbitrarily small delay perturbations, unlike the standard H-infinity norm. We opt…
This paper considers online switching control with a finite candidate controller pool, an unknown dynamical system, and unknown cost functions. The candidate controllers can be unstabilizing policies. We only require at least one candidate controller to satisfy certain stability properties, but we do not know which one is stabilizing. We design an online algorithm that guarantees finite-gain stability throughout the duration of its execution. We also provide a sublinear policy regret guarantee compared with the optimal stabilizing candidate controller. Lastly, we numerically test our algorithm…
An eigenvalue based framework is developed for the stability analysis and stabilization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations are analyzed and their stability properties are studied, taking into account the effect of small delay perturbations. Subsequently, numerical methods for stability assessment and for designing stabilizing controllers with a prescribed structure or order, based on a direct optimization approach, are briefly addressed. The effectiveness of the approach is ill…
This paper presents an algebraic technique to compute the maximum time-delay that can be accepted in the control loop of a Brushless DC Motor (BLDCM) speed controller before the closed loop response becomes unstable. Using a recently proposed time-delay stability analysis methodology, we derive accurate stability conditions for the BLDCM speed controller. The results of applying the new method show that tuning the PI controller for very fast response in the order of magnitude of the BLDCM mechanical time constant cause the time-delay to significantly affect the system stability.
An eigenvalue based framework is developed for the H-infinity norm analysis and its norm minimization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations (DDAEs). For these equations H-infinity norms are analyzed and their sensitivity with respect to small delay perturbations is studied. Subsequently, numerical methods for the H-infinity norm computation and for designing controllers minimizing the H-infinity norm with a prescribed structure or order, based on a direct optimization approach, are briefly addressed. The effectiveness of th…
In networked control systems, often the sensory signals are quantized before being transmitted to the controller. Consequently, performance is affected by the coarseness of this quantization process. Modern communication technologies allow users to obtain resolution-varying quantized measurements based on the prices paid. In this paper, we consider optimal controller synthesis of a Quantized-Feedback Linear-Quadratic-Gaussian (QF-LQG) system where the measurements are to be quantized before being transmitted to the controller. The system is presented with several choices of quantizers, along w…
Electrolysis systems use proportional-integral-derivative (PID) temperature controllers to maintain stack temperatures around set points. However, heat transfer delays in electrolysis systems cause manual tuning of PID temperature controllers to be time-consuming, and temperature oscillations often occur. This paper focuses on the design of the PID temperature controller for an alkaline electrolysis system to achieve fast and stable temperature control. A thermal dynamic model of an electrolysis system is established in the frequency-domain for controller designs. Based on this model, the temp…
Direct Adaptive Controller for Uncertain MIMO Dynamic Systems with Time-varying Delay and Dead-zone Inputs
South China University of Technology（华南理工大学）；Massachusetts Institute of Technology (MIT)（麻省理工学院）；Northeastern University（东北大学）；University of Science and Technology Beijing（北京科技大学）
We address the problem of sparsity-promoting optimal control of cyber-physical systems with feedback delays. The delays are categorized into two classes - namely, intra-layer delay, and inter-layer delay between the cyber and the physical layers. Our objective is to minimize the H2-norm of the closed-loop system by designing an optimal combination of these two delays along with a sparse state-feedback controller, while respecting a given bandwidth constraint. We propose a two-loop optimization algorithm for this. The inner loop, based on alternating directions method of multipliers (ADMM), han…
In this note, we present an effective solution to the stabilization of linear input delay systems subject to dissipative constraints while all the effect of input delay is compensated by a controller with novel structure. The method is inspired by the recent development in the mathematical treatment of distributed delays and predictor controllers, which are critical for the derivation of the solution. An important conceptual innovation is the use of a parameterized dynamical state feedback controller (DSFC), where the dimension of the controller equals the dimension of the control input. A suf…
This paper studies stochastic aperiodic stabilization of a networked control system (NCS) consisting of a continuous-time plant and a discrete-time controller. The plant and the controller are assumed to be connected by communication channels with i.i.d. time-varying delays. The delays are theoretically not required to be bounded even when the plant is unstable in the deterministic sense. In our NCS, the sampling interval is supposed to be determined directly by such communication delays. A necessary and sufficient inequality condition is presented for designing a state-feedback controller sta…
This work addresses the synchronization/consensus problem of identical multi-agent system (MAS) where the agents' dynamics are linear and the communication network is arbitrarily switching among connected topologies. The approach uses a gain matrix of a special structure in a dynamic compensator for each agent. Under reasonable conditions, the approach ensures that consensus is reached when the gain is sufficiently large. This result holds for general linear systems including the case where agents have repeated unstable eigenvalues. The proposed controller structure can be seen as a special ca…
This paper presents a framework for the design and analysis of an $\mathcal{L}_1$ adaptive controller with a switching reference system. The use of a switching reference system allows the desired behavior to be scheduled across the operating envelope, which is often required in aerospace applications. The analysis uses a switched reference system that assumes perfect knowledge of uncertainties and uses a corresponding non-adaptive controller. Provided that this switched reference system is stable, it is shown that the closed-loop system with unknown parameters and disturbances and the $\mathca…
H-infinity controllers are frequently used in control theory due to their robust performance and stabilization. Classical H-infinity controller synthesis methods for finite dimensional LTI MIMO plants result in high-order controllers for high-order plants whereas low-order controllers are desired in practice. We design fixed-order H-infinity controllers for a class of time-delay systems based on a non-smooth, non-convex optimization method and a recently developed numerical method for H-infinity norm computations.
Practical adaptive control implementations where human pilots coexist in the loop are still uncommon, despite their success in handling uncertain dynamical systems. This is owing to their special nonlinear characteristics which lead to unfavorable interactions between pilots and adaptive controllers. To pave the way for the implementation of adaptive controllers in piloted applications, we propose an adaptive human pilot model that takes into account the time delay in the pilot's response while operating on an adaptive control system. The model can be utilized in the evaluation of adaptive con…
We present a delay-compensating control method that transforms exponentially stabilizing controllers for an undelayed system into a sample-based predictive controller with numerical integration. Our method handles both first-order and transport delays in actuators and trades-off numerical accuracy with computation delay to guaranteed stability under hardware limitations. Through hybrid stability analysis and numerical simulation, we demonstrate the efficacy of our method from both theoretical and simulation perspectives.
