Stochastic Packetized Model Predictive Control for Networked Control Systems Subjects to Time-delays and Dropouts
نویسندگان
چکیده
Introduccion. Networked Control Systems (NCS) are systems in which serial communication networks are used to exchange system information and control signals between various physical components of the systems that may be physically distributed. Major advantages of NCS include low cost, reduced weight and power requirements, simple installation and maintenance, and high reliability. Nonetheless, closing a control loop on a shared communication network introduces additional dynamics and constraints in the control problem. In addition to being bit-rate limited [1], [2], practical communitacion channels are commonly affected by packet dropouts and time delays, mainly due to transmission errors and waiting times to access the medium; see, e.g., [3]-[5] and the many references therein. To overcome these problems, it has been proposed to send from the controller a sequence of control signals that, appropriately buffered and scheduled at the actuator end, become a safeguard in case of delays or eventual packet dropouts. This concept naturally fits the model predictive control (MPC) paradigm. Although a significant body of research has developed different strategies combining MPC and buffering strategies there is still room for further research and improvements. On the one hand in works such as [6] or [7] neglect the effect of the network induced delays focusing the attention on the problem of packet dropouts, while in [8] only delays are considered. Further, in many works on MPC for NCS a deterministic approach is considered, yielding a worst-case approach. The present work considers both packet dropouts and random delays. We adopt a stochastic approach which allows to improve the control performance provided that the statistical distribution of the delays are known. Notation. We write R for the real numbers, N for {1,2, . . .}, and N0 for N∪{0}. The p× p identity matrix is denoted via Ip. For the column vector in Rp containing only ones we write 1p, whereas 0p = 0 ·1p. The norm of a vector x is denoted |x|. To denote the probability of an event Ω, we write Prob{Ω}. The conditional probability of Ω given Γ is denoted via Prob{Ω |Γ}. The expected value of a random variable ν given Γ, is denoted by E{ν |Γ}, whereas for the unconditional expectation we will write E{ν}. We use the same notation for random variables and their realizations.
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