Robust Tube MPC for Linear Systems With Multiplicative Uncertainty

Self Cite

Summary A distributed stochastic model predictive control algorithm is proposed for multiple linear subsystems with both parameter uncertainty and stochastic disturbances, which are coupled via probabilistic constraints. To handle the probabilistic constraints, the system dynamics is first decomposed into a nominal part and an uncertain part. The uncertain part is further divided into 2 parts: the first one is constrained to lie in probabilistic tubes that are calculated offline through the use of the probabilistic information on disturbances, whereas the second one is constrained to lie in polytopic tubes whose volumes are optimized online and whose facets' orientations are determined offline. By permitting a single subsystem to optimize at each time step, the probabilistic constraints are then reduced into a set of linear deterministic constraints, and the online optimization problem is transformed into a convex optimization problem that can be performed efficiently. Furthermore, compared to a centralized control scheme, the distributed stochastic model predictive control algorithm only requires message transmissions when a subsystem is optimized, thereby offering greater flexibility in communication. By designing a tailored invariant terminal set for each subsystem, the proposed algorithm can achieve recursive feasibility, which, in turn, ensures closed‐loop stability of the entire system. A numerical example is given to illustrate the efficacy of the algorithm.

“…From the fact that

\lim_{l \to \infty} v_{p, l}^{false(j false)} = 0

\lim_{l \to \infty} f_{p, l} = 0

, and

\lim_{l \to \infty} f_{c p, l} = 0

, the existence of these terminal sets, ie, the existence of

{\overset{θ}{true}}_{p}

for each subsystem satisfying , can be ensured if l = N 1 − N is chosen to be sufficiently large and the following conditions are satisfied:

\frac{false‖ M_{p} ‖_{\infty} \max_{j} {(‖‖, {\overset{d}{true}}_{p}^{false(j false)})}_{\infty}}{1 - \max_{j} {(‖‖, M_{p}^{false(j false)})}_{\infty}} < h_{p} - {\overset{β}{true}}_{p}, \forall p \in scriptP,

true \sum_{p = 1}^{N_{p}} \frac{false‖ M_{c p} ‖_{\infty} \max_{j} {(‖‖, {\overset{d}{true}}_{p}^{false(j false)})}_{\infty}}{1 - \max_{j} {(‖‖, M_{p}^{false(j false)})}_{\infty}} < b_{c} - {\overset{κ}{true}}_{c}, \forall c \in scriptC .

…”

Section: Centralized Smpc Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed stochastic MPC for systems with parameter uncertainty and disturbances

Xia

Gao

et al. 2018

Self Cite

“…The first two elements of the disturbance vector v z in (26), namely, w andx * , are confined to sets centred around the origin (see the description of w in Section 2 and the bound oñ x * in (23), respectively). The third and fourth elements of v, ie,x andū, belong to sets centred at x s and u s , respectively (see (8)). Hence, the disturbance term can be bounded as…”

Section: Healthy Set Computationmentioning

confidence: 99%

“…While MPC provides a widely effective means of computing an “optimal” control law in the presence of constraints for linear systems (see, eg, the work of Goodwin et al), the effects of model uncertainty projected over the evolution of predicted states can cause the computational burden to grow exponentially with the prediction horizon. This difficulty can be overcome through the use of tube‐based MPC (see, eg, the work of Fleming et al), whereby one can recursively define tubes with cross‐sections that will contain the predicted state trajectory. Knowing that the predicted states lie in sets (cross‐sections of the “tube”), it is possible to formulate conditions that guarantee satisfaction of hard constraints (see, eg, the work of Rawlings and Mayne).…”

Section: Introductionmentioning

confidence: 99%

Fault‐tolerant fusion‐based MPC with sensor recovery for constrained LPV systems

McCloy

Doná

Serón

2018

Summary In this paper, we present a robust fault‐tolerant control scheme for constrained multisensor linear parameter‐varying systems, subject to bounded disturbances, that utilises multiple sensor fusion. The closed‐loop scheme consists of a tube model predictive control‐based feedback tracking controller and sensor‐estimate fusion strategy, which allows for the reintegration of previously faulty sensors. The active fault‐tolerant fusion‐based mechanism tracks the healthy‐faulty transitions of suitable residual variables by means of set separation and precomputed transition times. The sensor‐estimate pairings are then reconfigured based on available healthy sensors. Under the proposed scheme, robust preservation of closed‐loop system boundedness is guaranteed for a wide range of sensor fault situations. An example is presented to illustrate the performance of the fault‐tolerant control strategy.

“…The first control input of the sequence is applied to the plant at the current state and the process is repeated, which provides an effective way to approximate the optimal solution. 2,3 In the real control process with constraints and disturbances, MPC provides a suitable method to overcome the potential performance degradation and stability problems. [4][5][6][7] In published literatures on MPC, there are many instructive results to reduce the impacts of uncertainty and disturbances.…”

Section: Introductionmentioning

confidence: 99%

Robust event‐triggered model predictive control for constrained linear continuous system

Luo

Xia

Sun

2018

Model predictive control (MPC) is capable to deal with multiconstraint systems in real control processes; however, the heavy computation makes it difficult to implement. In this paper, a dual-mode control strategy based on event-triggered MPC (ETMPC) and state-feedback control for continuous linear time-invariant systems including control input constraints and bounded disturbances is developed. First, the deviation between the actual state trajectory and the optimal state trajectory is computed to set an event-triggered mechanism and reduce the computational load of MPC. Next, the dual-mode control strategy is designed to stabilize the system. Both recursive feasibility and stability of the strategy are guaranteed by constructing a feasible control sequence and deducing the relationship of parameters, especially the inter-event time and the upper bound of the disturbances. Finally, the theoretical results are supported by numerical simulation. In addition, the effects of the parameters are discussed by simulation, which gives guidance to balance computational load and control performance. KEYWORDSbounded disturbances, continuous LTI system, event-triggered, input constraints, model predictive control 1216