State control in networked control systems under packet drops and limited transmission bandwidth

The widespread proliferation of wireless sensor networks is revolutionizing our capabilities of monitoring and controlling the environment. The wireless connection of spatially distributed sensors, controllers and actuators poses challenges to the control system, due to packet drops, delays and measurements quantization, as well as to the wireless network resource allocator. These challenges push for a cross-layer design of communication and estimation/control systems. In this paper, assuming a TCP-like protocol between controller and actuator, we solve the problem of optimum control around a target state for a stable system in case of both packet drops and signal quantization. Generalization for unstable systems is also given in case of negligible quantization error. Moreover we propose a general framework for cross-layer optimization of signal quantization and network resource allocation. Here our main contributions are on i) quantizer design (how many bits to allocate for signal quantization), ii) network resource allocation (bit-rate for each radio link) and iii) choice of the transmission mode (constellation and channel coding rate). As application example, we consider a simple scalar, stable system and compare network resource allocation in the presence of i) low-cost sensors using a fix modulation and ii) long-term future sensors capable of rate adaptation. Interestingly, almost optimal control is achievable with small bandwidth transmissions and simple BPSK, supporting the use of low-cost sensors in applications dealing with state control around a target state trajectory.