Simultaneous nonlinear model predictive control and state estimation

Copp, David A.; Hespanha, J.P.

doi:10.1016/j.automatica.2016.11.041

Cited by 61 publications

(43 citation statements)

References 32 publications

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“…Our estimation and control approach combines MPC and MHE as discussed in the works of Copp and Hespanha,() where the MPC and MHE optimization objectives are incorporated within a single min‐max optimization problem, the solution of which simultaneously characterizes solutions to the MHE and MPC subproblems. We formulate the MPC/MHE problem as a finite‐horizon min‐max optimization problem, to be solved at each time t , of the following form:

\min_{u_{t : t + M - 1}} \max_{\begin{matrix} 0 \\ x_{t - L}, \\ d_{t - L : t + T - 1} \end{matrix}} J_{t} ((), x_{t - L}, u_{t - L : t - 1}, u_{t : t + M - 1}, d_{t - L : t + T - 1}, n_{t - L : t}),

with cost function

J_{t} false(\cdot false) : = true \sum_{k = t + 1}^{t + T} c {false(C x_{k} false)}^{2} + true \sum_{k = t}^{t + M - 1} λ_{u} u_{k}^{2} - true \sum_{k = t - L}^{t + T - 1} λ_{d} d_{k}^{2} - true \sum_{k = t - L}^{t} λ_{n} n_{k}^{2},

and subject to

\begin{matrix} alignleft \\ align-1 x_{k + 1} & align-2 = A x_{k} + B u_{k} + D d_{k} & \forall k \in {double-struckZ}_{t - L}^{t + T - 1} \end{matrix}

…”

Section: Estimation and Control Approachmentioning

confidence: 99%

“…For more details on the formulation and stability of this MPC/MHE approach, we refer the reader to see other works. ()…”

Section: Estimation and Control Approachmentioning

confidence: 99%

“…More details and theoretical results regarding this approach to combine MPC with MHE can be found in the works of Copp and Hespanha. () A particular primal‐dual‐like interior‐point method was developed by the authors to numerically solve these optimization problems, and details about this method can be found in the work of Copp and Hespanha . In addition, this MPC/MHE approach allows the estimation of unknown or uncertain model parameters .…”

Section: Estimation and Control Approachmentioning

confidence: 99%

“…Fortunately, the optimization problem corresponding to the MPC/LO approach can be formulated and solved as a quadratic program, and the clinical version of the controller has been implemented and tested on a tablet computer during clinical trials (for more details, see the work of Gondhalekar et al). The MPC/MHE approach can be solved very efficiently using a primal‐dual‐like interior‐point method presented in the work of Copp and Hespanha . In both cases, the sample period T s =5 minutes is sufficiently long (excessive by multiple orders of magnitude) to compute a solution to the optimization problems.…”

Section: Estimation and Control Approachmentioning

confidence: 99%

“…Our estimation and control approach combines MPC and MHE as discussed in the works of Copp and Hespanha, 22,23 where the MPC and MHE optimization objectives are incorporated within a single min-max optimization problem, the solution of which simultaneously characterizes solutions to the MHE and MPC subproblems. We formulate the MPC/MHE problem as a finite-horizon min-max optimization problem, to be solved at each time t, of the following form:…”

Section: Combined Mpc and Mhementioning

confidence: 99%

See 4 more Smart Citations

Simultaneous model predictive control and moving horizon estimation for blood glucose regulation in Type 1 diabetes

Copp

Linares

Hespanha

2017

Optim Control Appl Methods

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Summary A new estimation and control approach for the feedback control of an artificial pancreas to treat Type 1 diabetes mellitus is proposed. In particular, we present a new output‐feedback predictive control approach that simultaneously solves the state estimation and control objectives by means of a single min‐max optimization problem. This involves optimizing a cost function with both finite forward and backward horizons with respect to the unknown initial state, unmeasured disturbances and noise, and future control inputs and is similar to simultaneously solving a model predictive control (MPC) problem and a moving horizon estimation (MHE) problem. We incorporate a novel asymmetric output cost to penalize dangerous low blood glucose values more severely than less harmful high blood glucose values. We compare this combined MPC/MHE approach to a control strategy that uses state‐feedback MPC preceded by a Luenberger observer for state estimation. In‐silico results showcase several advantages of this new simultaneous MPC/MHE approach, including fewer hypoglycemic events without increasing the number of hyperglycemic events, faster insulin delivery in response to a meal consumption, and shorter insulin pump suspensions, resulting in smoother blood glucose trajectories.

show abstract

\min_{u_{t : t + M - 1}} \max_{\begin{matrix} 0 \\ x_{t - L}, \\ d_{t - L : t + T - 1} \end{matrix}} J_{t} ((), x_{t - L}, u_{t - L : t - 1}, u_{t : t + M - 1}, d_{t - L : t + T - 1}, n_{t - L : t}),

with cost function

J_{t} false(\cdot false) : = true \sum_{k = t + 1}^{t + T} c {false(C x_{k} false)}^{2} + true \sum_{k = t}^{t + M - 1} λ_{u} u_{k}^{2} - true \sum_{k = t - L}^{t + T - 1} λ_{d} d_{k}^{2} - true \sum_{k = t - L}^{t} λ_{n} n_{k}^{2},

and subject to

\begin{matrix} alignleft \\ align-1 x_{k + 1} & align-2 = A x_{k} + B u_{k} + D d_{k} & \forall k \in {double-struckZ}_{t - L}^{t + T - 1} \end{matrix}

…”

Section: Estimation and Control Approachmentioning

confidence: 99%

“…For more details on the formulation and stability of this MPC/MHE approach, we refer the reader to see other works. ()…”

Section: Estimation and Control Approachmentioning

confidence: 99%

Section: Estimation and Control Approachmentioning

confidence: 99%

Section: Estimation and Control Approachmentioning

confidence: 99%

Section: Combined Mpc and Mhementioning

confidence: 99%

See 3 more Smart Citations

Simultaneous model predictive control and moving horizon estimation for blood glucose regulation in Type 1 diabetes

Copp

Linares

Hespanha

2017

Optim Control Appl Methods

Self Cite

View full text Add to dashboard Cite

show abstract

Simultaneous robust model predictive control and state estimation for nonlinear systems with state‐ and input‐dependent uncertainties

Badfar,

Safavi

2024

Asian Journal of Control

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The convergence and stability of uncertain nonlinear systems is a challenging problem in the nonlinear control area. Besides, in many practical cases, all states are not measurable and are affected by measurement noise. Based on this motivation, the first objective of this paper is to design a novel output feedback robust model predictive control approach for nonlinear systems with state‐ and input‐dependent uncertainties and measurement noise. This approach combines state estimation and robust model predictive control (MPC) into one min–max optimization and by solving the optimization, these two tasks are performed simultaneously. The studied nonlinear system comprises a linear part, a nonlinear part, and a function that denotes the state‐ and input‐dependent uncertainties. Therefore, the other objective is to reduce the computational complexity; thus, the system's nonlinear term and the aforementioned uncertainties are converted into additional disturbances. Subsequently, the optimization problem becomes a quadratic form, which leads to global convergence with the appropriate selection of objective function weights. Besides, this paper explores the convergence of the closed‐loop system states and the sufficient synthesis conditions to guarantee input‐to‐state stability. The implementation on a numerical example and a CSTR process demonstrate the applicability and reliability of the proposed approach.

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Simultaneous moving horizon estimation and control for nonlinear systems subject to bounded disturbances

Deniz

Sánchez

Murillo

et al. 2023

Intl J Robust & Nonlinear

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In this work, we address the output-feedback control problem for nonlinear systems under bounded disturbances using a moving horizon approach. The controller is posed as an optimisation-based problem that simultaneously estimates the state trajectory and computes future control inputs. It minimizes a criterion that involves finite backward and forward horizons with respect to the unknown initial state, measurement noises and control input variables.The main novelty of this work relies on linking the lengths of the forward and backward windows with the closed-loop stability, assuming detectability and decoding sufficient conditions to assure system stabilizability. It leads to a formulation that does not require to be a Control Lyapunov Function for the terminal cost of the controller. Simulation examples are carried out to compare the performance of solving simultaneously and independently the estimation and control problems. Furthermore, the examples show how the controller influences the length of the estimation window through its gain.

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Simultaneous nonlinear model predictive control and state estimation

Cited by 61 publications

References 32 publications

Simultaneous model predictive control and moving horizon estimation for blood glucose regulation in Type 1 diabetes

Simultaneous model predictive control and moving horizon estimation for blood glucose regulation in Type 1 diabetes

Simultaneous robust model predictive control and state estimation for nonlinear systems with state‐ and input‐dependent uncertainties

Simultaneous moving horizon estimation and control for nonlinear systems subject to bounded disturbances

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