Dynamic Optimization for Switched Time-Delay Systems with State-Dependent Switching Conditions

Liu, Chongyang; Loxton, Ryan; Lin, Qun; Teo, Kok Lay

doi:10.1137/16m1070530

Cited by 50 publications

(18 citation statements)

References 29 publications

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“…In this section, based on [5,[24][25][26], we give a numerical method to solve the optimality system (12). Let there exists a step size h > 0 and integers (n, b) ∈ N 2 with τ = bh and T − t 0 = nh.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Optimal control of a delayed smoking model with immigration

Sun

Jia

2019

Journal of Biological Dynamics

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In this paper, we formulate a smoking model with delay and immigration, and the possibility of optimal controls both over the susceptible and heavy problem smoker subjects is assumed. The existence of the optimal control pair is also proved. We derive the optimality condition via the Pontryagin's maximum principle with delay and obtain the existence of the optimal solution. Numerical simulation is given. Numerical simulations are made to support the main results.

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Section: Numerical Simulationsmentioning

confidence: 99%

Optimal control of a delayed smoking model with immigration

Sun

Jia

2019

Journal of Biological Dynamics

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“…Nacem et al [17] proposed a PID based method. For more details, the readers are referred to [26]- [28].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Model Predictive Control for the Set Point Tracking of Unmanned Surface Vehicles

Yuan

Cai

et al. 2020

IEEE Access

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An unmanned surface vehicles (USV) set point tracking problem is investigated in this paper. The stochastic model predictive control (SMPC) scheme is utilized to design the controller in order to reject the environment disturbances and meet the physical constraints. The design problem is formulated as a chance-constrained stochastic optimization problem, which is non-convex. Thus, the problem is computationally prohibitive. For this, the convex conditional value at risk (CVaR) approximation is introduced to convert the chance constraints into deterministic convex constraints. The converted constraints are then further transformed into the second order cone (SOC) constraints. Therefore, the proposed method is computationally tractable and hence can be implemented online. A numerical example is provided to illustrate the effectiveness of the proposed method. INDEX TERMS Unmanned surface vehicles (USV), set point tracking, stochastic model predictive control, chance constraints, conditional value at risk (CVaR).

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“…By assuming that transports of glycerol and l,3-PD across cell membrane are both the active transport and the passive diffusion, parameter identification problem was discussed in [5]. To maximize concentration of 1,3-PD in fed-batch fermentation, optimal switching control [11,12,13,14,15], multiobjective optimal control [16,20], robust multi-objective optimal control [17] and time-delayed optimal control [18] were reported. Open loop inputs and pH logic control was considered in [32,33].…”

mentioning

confidence: 99%

Multistage optimal control for microbial fed-batch fermentation process

Sun

Gong

et al. 2022

JIMO

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In this paper, we consider multistage optimal control of bioconversion glycerol to 1,3-propanediol(1,3-PD) in fed-batch fermentation process. To maximize the productivity of 1,3-PD, the whole fermentation process is divided into three stages according to the characteristics of microbial growth. Stages 2 and 3 are discussed mainly. The main aim of stage 2 is to restrict accumulation of 3-hydroxypropionaldehyde and maximize the biomass in the shortest time, and the purpose of stage 3 is to get high productivity of 1,3-PD. With these different objectives, multi-objective optimal control problems are proposed in stages 2 and 3. In order to solve the above optimal control problems, the multi-objective problems are transformed to the corresponding single-objective problems using the mass balance equation of biomass and normalization of the objective. Furthermore, the single-objective optimal control problems are transformed to two-level optimization problems by the control parametrization technique. Finally, numerical solution methods combined an improved Particle Swarm Optimization with penalty function method are developed to solve the resulting optimization problems. Numerical results show that the productivity of 1,3-PD is higher than the reported results.

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Dynamic Optimization for Switched Time-Delay Systems with State-Dependent Switching Conditions

Cited by 50 publications

References 29 publications

Optimal control of a delayed smoking model with immigration

Optimal control of a delayed smoking model with immigration

Stochastic Model Predictive Control for the Set Point Tracking of Unmanned Surface Vehicles

Multistage optimal control for microbial fed-batch fermentation process

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