W. P. Maurice H. Heemels

Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance

There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.

String stability of interconnected vehicles under communication constraints

In this paper, we present a novel modelling and string stability analysis method for an interconnected vehicle string in which information exchange takes place via wireless communication. The usage of wireless communication introduces time-varying sampling intervals, delays, and communication constraints of which the impact on string stability requires a careful analysis. In particular, we study a Cooperative Adaptive Cruise Control (CACC) system which regulates inter-vehicle distances in a vehicle string and utilizes information exchange between vehicles through wireless communication in addition to local sensor measurements. The propagation of disturbances through the interconnected vehicle string is inspected by using the notion of so-called string stability which is formulated here in terms of an ℒ2-gain requirement from disturbance inputs to controlled outputs. This paper provides conditions on the uncertain sampling intervals and delays under which string stability can still be guaranteed. These results support the design of CACC systems that are robust to uncertainties introduced by wireless communication.

Tracking Control for Nonlinear Networked Control Systems

We investigate the tracking control of nonlinear networked control systems (NCS) affected by disturbances. We consider a general scenario in which the network is used to ensure the communication between the controller, the plant and the reference system generating the desired trajectory to be tracked. The communication constraints induce non-vanishing errors (in general) on the feedforward term and the output of the reference system, which affect the convergence of the tracking error. As a consequence, available results on the stabilization of equilibrium points for NCS are not applicable. Therefore, we develop an appropriate hybrid model and we give sufficient conditions on the closed-loop system, the communication protocol and an explicit bound on the maximum allowable transmission interval guaranteeing that the tracking error converges to the origin up to some errors due to both the external disturbances and the aforementioned non-vanishing network-induced errors. The results cover a large class of the so-called uniformly globally asymptotically stable protocols which include the well-known round-robin and try-once-discard protocols. We also introduce a new dynamic protocol suitable for tracking control. Finally, we show that our approach can be used to derive new results for the observer design problem for NCS. It has to be emphasized that the approach is also new for the particular case of sampled-data systems.

Further Input-to-State Stability Subtleties for Discrete-Time Systems

This technical note considers input-to-state stability analysis of discrete-time systems using continuous Lyapunov functions. The main result reveals a relation between existence of a continuous Lyapunov function and inherent input-to-state stability on compact sets with respect to both inner and outer perturbations. If the Lyapunov function is K∞-continuous, the result applies to unbounded sets as well.

Switching Control in Vibration Isolation Systems

In this paper, a switching control approach for active vibration isolation systems is proposed. The switching involves two regimes. In the first regime, no feedback control is applied thereby giving a low sensitivity to noise. In the second regime, active control induces improved disturbance rejection properties, but at the cost of increased noise sensitivity. Conditions for the stability of the switching closed-loop system are formulated whereas the stability analysis provides design rules for tuning the switching controller. Given this novel active vibration isolation approach, improved isolation performance is obtained with substantially less control authority in comparison to the case of linear (or non-switching) feedback control. Performance analysis is based on multi-resolution time-frequency analysis using measurements taken from a commercial vibration isolation system.

Robust Global Stabilization of the DC-DC Boost Converter via Hybrid Control

In this paper, we consider the modeling and (robust) control of a DC-DC Boost converter. In particular, we derive a mathematical model consisting of a constrained switched differential inclusion that includes all possible modes of operation of the converter. The obtained model is carefully selected to be amenable for the study of various important robustness properties. For this model, we design a control algorithm that induces robust, global asymptotic stability of a desired output voltage value. The guaranteed robustness properties ensure proper operation of the converter in the presence of noise in the state, unmodeled dynamics, and spatial regularization to reduce the high rate of switching. The establishment of these properties is enabled by recent tools for the study of robust stability in hybrid systems. Simulations illustrating the main results are included.

Tracking control for hybrid systems via embedding of known reference trajectories

We study the problem of designing controllers to track time-varying state trajectories for plants modeled as hybrid dynamical systems, which are systems with both continuous and discrete dynamics. The reference trajectories are given by functions that may exhibit jumps. The class of controllers considered are also modeled as hybrid systems. These are designed to guarantee stability of tracking and that the difference between the plants state and the reference trajectory converges to zero. Using recently developed tools for the study of asymptotic stability in hybrid systems, we recast the tracking problem as the problem of stabilizing a closed set and derive conditions for the design of tracking controllers for hybrid reference trajectories with the property that the jump times of the plant coincide with those of the given reference trajectories. The approach is illustrated in examples.

Linear Quadratic Regulation of Switched Systems Using Informed Policies

The problem of designing a switching and control policy for regulating the state of a switched linear system to zero while minimizing a quadratic cost appears in numerous applications. However, obtaining the optimal policy is in general computationally intractable. Here, we propose a class of suboptimal policies that exploit information, in terms of upper or lower bounds, on the optimal cost. We analyze the performance of these novel policies, obtaining new bounds on the optimal cost which are tighter than the initial ones. The usefulness of these policies and performance bounds is illustrated in the context of resource-aware control.

Event-Triggered Control for String-Stable Vehicle Platooning

Cooperative adaptive cruise control (CACC) is a promising technology that is proven to enable the formation of vehicle platoons with small inter-vehicle distances, while avoiding amplifications of disturbances along the vehicle string. As such, CACC systems can potentially improve road safety, traffic throughput and fuel consumption due to the reduction in aerodynamic drag. Dedicated short range communication (DSRC) is a key ingredient in CACC systems to overcome the limitations of onboard sensors. However, wireless communication also involves inevitable network-induced imperfections, such as a limited communication bandwidth and time-varying transmission delays. Moreover, excessive utilization of communication resources jeopardizes the reliability of the DSRC channel. The latter might restrict the minimum time gap that can be realized safely. As a consequence, to harvest all the benefits of CACC, it is important to limit the communication to only the information that is actually required to establish a (string-)stable platoon over the wireless network and to avoid unnecessary transmissions. For this reason, an event-triggered control scheme and communication strategy is developed that takes into account the aforementioned network-induced imperfections and that aims to reduce the utilization of communication resources, while maintaining the desired closed-loop performance properties. The resulting

Stability analysis of networked control systems with direct-feedthrough terms: Part I - the nonlinear case

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