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We consider a wireless control system where sensors transmit their measurements to a controller over a fading channel. We assume that each sensor is equipped with a rechargeable battery and can harvest energy from the environment or other energy sources. To predict the harvested energy, we consider a stationary Markovian model conditioned on a scenario and estimate the unknown parameters based on empirical measurements. The transmission energy is assumed to be inversely proportional to the communication channel gain, which is described by a compound distribution. To increase energy efficiency, we use a continuous event-trigger allowing the sensors to transmit new data only when certain conditions are satisfied. Finally, we analyze the exponential stability of the closed-loop nonlinear system with multiple sector-bounded nonlinearities based on the input-delay method and Lyapunov–Krasovskii technique.

We investigate the optimal power control for multisensor estimation of correlated random Gaussian sources. A group of wireless sensors obtains local measurements and transmits them to a remote fusion center (FC), which reconstructs the measurements using the minimum mean-square error estimator. All the sensors are equipped with an energy harvesting module and a transceiver unit for wireless, directed energy sharing between neighboring sensors. The sensor batteries are of finite storage capacity and prone to energy leakage. Our aim is to find optimal power control strategies, which determine the energies used to transmit data to the FC and shared between sensors, so as to minimize the long-term average distortion over an infinite horizon. We assume centralized causal information of the harvested energies and channel gains, which are generated by independent finite-state stationary Markov chains. The optimal power control policy is derived using a stochastic predictive control formulation. We also investigate the structure of the optimal solution, a Q-learning based suboptimal power control scheme and two computationally simple and easy-to-implement heuristic policies. Extensive numerical simulations illustrate the performance of the considered policies.

We consider the problem of control and remote state estimation with battery constraints and energy harvesting at the sensor (transmitter) under DoS/jamming attacks. We derive the optimal non-causal energy allocation policy that depends on current properties of the channel and on future energy usage. The performance of this policy is analyzed under jamming attacks on the wireless channel, in which the assumed and the true channel gains differ, and we show that the resulting control cost is not monotonic with respect to the assumed channel gain used in the transmission policy. Additionally, we show that, in case there exists a stabilizing policy, then the optimal causal policy ensures stability of the estimation process. The results were illustrated for non-causal and causal energy allocation policies under different jamming attacks.

In this paper we present a method of bidirectional control of a vehicle string that achieves l2 weak string stability. Previous work required short-range communications between vehicles within the string. Here, we utilise some recent results on integral action to remove the requirement of communications altogether.

Sufficient conditions guaranteeing Lyapunov stability, asymptotic stability and exponential stability of nonlinear two-dimensional continuous–discrete systems are proposed. Special attention is paid to neutrally stable systems such as some two-dimensional system descriptions of vehicle platoons, which may be stable or asymptotically stable but never exponentially stable. Our conditions for Lyapunov stability and asymptotic stability only require the corresponding two-dimensional Lyapunov function to have a negative semidefinite divergence. They are thus suitable for the analysis of non-exponential versions of 2D stability. Examples are given to illustrate the results.

A sensor computes a state estimate of a closed loop linear control system. The state estimate is packetized and sent to the controller in the receiver block over a randomly time-varying (fading) packet dropping link. The receiver sends an ACK/NACK packet to the transmitter over a perfect feedback channel. The energy used in packet transmission depletes a battery of limited capacity at the sensor. The battery is replenished by an energy harvester, which has access to a source of everlasting but random harvested energy. Further, the energy harvesting and the fading channel gain processes are described as finite-state Markov chain models. The objective is to design an optimal energy allocation policy at the transmitter and an optimal control policy at the receiver so that an average infinite horizon linear quadratic Gaussian (LQG) control cost is minimised. It is shown that a separation principle holds, the optimal controller is linear, the Kalman filter at the sensor is optimal, and the optimal energy allocation policy at the transmitter can be obtained via solving the Bellman dynamic programming equation to a Markov decision process based stochastic control problem. A Q-learning algorithm is used to approximate the optimal energy allocation policy. Numerical simulations illustrate that the dynamic programming based policies outperform the simple heuristic policies.

In this paper, we show how heterogeneous bidirectional vehicle strings can be modelled as port-Hamiltonian systems. Analysis of stability and string stability within this framework is straightforward and leads to a better understanding of the underlying problem. Nonlinear local control and additional integral action is introduced to design a suitable control law guaranteeing l 2 string stability of the system with respect to bounded disturbances.

This paper studies a closed loop linear control system over a lossy communication link. A sensor computes a state estimate of the observed discrete-time system and sends it (in the form of packetized transmission) to the controller in the receiver block over a randomly time-varying (fading) packet dropping link. The receiver sends an ACK/NACK packet to the transmitter over an acknowledgement channel which might also be prone to packet loss. It is assumed that the energy used in packet transmission depletes a battery of limited capacity at the sensor, but is also replenished by an energy harvester which has access to a source of everlasting but random harvested energy. Under an assumption of finite-state Markov chain models of the energy harvesting and the fading channel gain processes, the objective is to design an optimal energy allocation policy at the transmitter and an optimal control policy at the receiver so that an average infinite horizon linear quadratic Gaussian (LQG) control cost is minimized. It is shown that in the case of perfect channel feedback a separation principle holds, the optimal LQG controller is linear and the optimal energy allocation policy at the transmitter can be obtained via solving the Bellman dynamic programming equation. A Q-learning algorithm is used to approximate the optimal energy allocation policy in case the system parameters are unknown. Numerical simulation examples show that the dynamic programming based policies outperform various simple heuristic policies, especially at higher battery capacities. Refereed/Peer-reviewed

This paper gives results on stability and asymptotic stability of two-dimensional systems using linear matrix inequalities (LMIs). Despite a long history of research in this area, systems with singularities on the stability boundary (SSB) have received limited attention because they cannot produce a sign definite solution to the required LMI. However, 2D systems describing some classes of models of vehicle platoons generically involve an SSB. Therefore, commonly used definitions for (asymptotic) stability and strict LMI conditions are not suitable to discuss the stability of these systems. It is shown that the existence of a negative semidefinite solution together with simple additional conditions is sufficient to guarantee asymptotic stability. Thus, the stability conditions discussed here can be used to study a wider range of dynamical systems, including systems with singularities on the stability boundary (SSB), which cannot be exponentially stable. A unified framework is used to analyse continuous-continuous, continuous-discrete and discrete-discrete systems simultaneously.

This paper considers a string of vehicles where the local control law uses the states of the vehicle's immediate predecessor and follower. The coupling towards the preceding vehicle can be chosen different to the coupling towards the following vehicle, which is often referred to as an asymmetric bidirectional string. Further, the asymmetry for the velocity coupling can be chosen differently to the asymmetry in the position coupling. It is investigated how the effect of disturbance on the control errors in the string depends on the string length. It is shown, that in case of symmetric position coupling and asymmetric velocity coupling, linear scaling can be achieved. For symmetric interaction in both states, i.e., in symmetric bidirectional strings, the errors scale quadratically in the number of vehicles. When the coupling in position is asymmetric, exponential scaling may occur or the system might even become unstable. The paper thus gives a comprehensive overview of the achievable performance in linear, asymmetric, bidirectional platoons. The results reveal that symmetry in the position coupling and asymmetry in velocity coupling qualitatively improves the performance of the string. Extensive numerical results illustrate the theoretical findings., submitted, 10 pages

This paper studies a closed loop linear control system. The sensor computes a state estimate and sends it to the controller/actuator in the receiver block over a randomly fading packet dropping link. The receiver sends an ACK/NACK packet to the transmitter over a link. It is assumed that the transmission energy per packet at the sensor depletes a battery of limited capacity, replenished by an energy harvester. The objective is to design an optimal energy allocation policy and an optimal control policy so that a finite horizon LQG control cost is minimized. It is shown that in case the receiver to sensor feedback channel is free of errors, a separation principle holds. Hence, the optimal LQG controller is linear, the Kalman filter is optimal and the optimal energy allocation policy is obtained via solving a backward dynamic programming equation. In case the feedback channel is erroneous, the separation principle does not hold. In this case, we propose a suboptimal policy where the controller still uses a linear control, and the transmitter minimizes an expected sum of the trace of an estimated receiver state estimation error covariance matrix. Simulations are used to illustrate the relative performance of the proposed algorithms and various heuristic algorithms for both the perfect and imperfect feedback cases. It is seen that the dynamic programming based policies outperform the simple heuristic policies by a margin. Refereed/Peer-reviewed

Stability of nonlinear 2D continuous-discrete systems is shown using Lyapunov stability theory and iISS. The proposed stability conditions are applicable with non-positive divergence of the Lyapunov function. The results are used to rigorously prove string stability of a nonlinear vehicle string with variable time headway.

It is shown how some classes of symmetric bidirectional heterogeneous vehicle strings can be modelled using a Hamiltonian framework. Hamiltonian systems theory is applied to show stability and string stability of certain vehicle strings. We also indicate how this analysis might be extended to classes of nonlinear controllers.

Vehicle strings can be modelled as continuous-discrete 2D systems. However, every such 2D system includes a structural nonessential singularity on the stability boundary and special care is needed to analyse BIBO stability of the system. A unidirectional vehicle string with communication range 2 is analysed and simulated.