A new approach to design asymptotically stabilizing control and adaptive control

Skandari, Mohammad Hadi Noori; Nazemi, Alireza

doi:10.1002/oca.2458

Cited by 6 publications

(9 citation statements)

References 39 publications

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“…To impose an optimal chemo‐drug dose, the PS method can be used [22 ]. In this method, the original non‐linear control system is formulated to an infinite‐horizon optimal control (IHOC).…”

Section: Chemotherapy Using the Ps Methodsmentioning

confidence: 99%

“…Lemma 1 Suppose that

τ_{1} = - 1 < τ_{2} < \dots < τ_{N} < 1

are the LGR collocation points on the intervals

τ \in ()[, - 1, 1)

. Then, there exists a unique set of quadrature weights

{\{w_{k}\}}_{k = 1}^{N}

such that for any polynomial

q false(\cdot false)

of degree

2 ()(, N - 1)

or less, we have [22 ]

\int_{- 1}^{1} q (t) normald t = \sum_{k = 1}^{N} w_{k} q (τ_{k}),

where

w_{k}

satisfies the following relation:

w_{k} = \frac{1 - τ_{k}}{N^{2} {()(, p_{N - 1} ()(, τ_{k}))}^{2}}, k = 1, \dots, N .

…”

Section: Chemotherapy Using the Ps Methodsmentioning

confidence: 99%

“…are the LGR collocation points on the intervals τ ∈ −1, 1 , which are the roots of the polynomialp( ⋅ ) = p N ( ⋅ ) + p N − 1 ( ⋅ ).Lemma Suppose that τ 1 = − 1 < τ 2 < ⋯ < τ N < 1 are the LGR collocation points on the intervals τ ∈ −1, 1 . Then, there exists a unique set of quadrature weights w k k = 1 N such that for any polynomial q( ⋅ ) of degree 2 N − 1 or less, we have[22] …”

mentioning

confidence: 99%

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Pseudo‐spectral method for controlling the drug dosage in cancer

Nazari

Skandari

2020

IET Systems Biology

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A mixed chemotherapy-immunotherapy treatment protocol is developed for cancer treatment. Chemotherapy pushes the trajectory of the system towards the desired equilibrium point, and then immunotherapy alters the dynamics of the system by affecting the parameters of the system. A co-existing cancerous equilibrium point is considered as the desired equilibrium point instead of the tumour-free equilibrium. Chemotherapy protocol is derived using the pseudo-spectral (PS) controller due to its high convergence rate and simple implementation structure. Thus, one of the contributions of this study is simplifying the design procedure and reducing the controller computational load in comparison with Lyapunov-based controllers. In this method, an infinite-horizon optimal control problem is proposed for a non-linear cancer model. Then, the infinite-horizon optimal control of cancer is transformed into a non-linear programming problem. The efficient Legendre PS scheme is suggested to solve the proposed problem. Then, the dynamics of the system is modified by immunotherapy is another contribution. To restrict the upper limit of the chemo-drug dose based on the age of the patients, a Mamdani fuzzy system is designed, which is not present yet. Simulation results on four different dynamics cases how the efficiency of the proposed treatment strategy.

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Section: Chemotherapy Using the Ps Methodsmentioning

confidence: 99%

“…Lemma 1 Suppose that

τ_{1} = - 1 < τ_{2} < \dots < τ_{N} < 1

are the LGR collocation points on the intervals

τ \in ()[, - 1, 1)

. Then, there exists a unique set of quadrature weights

{\{w_{k}\}}_{k = 1}^{N}

such that for any polynomial

q false(\cdot false)

of degree

2 ()(, N - 1)

or less, we have [22 ]

\int_{- 1}^{1} q (t) normald t = \sum_{k = 1}^{N} w_{k} q (τ_{k}),

where

w_{k}

satisfies the following relation:

w_{k} = \frac{1 - τ_{k}}{N^{2} {()(, p_{N - 1} ()(, τ_{k}))}^{2}}, k = 1, \dots, N .

…”

Section: Chemotherapy Using the Ps Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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Pseudo‐spectral method for controlling the drug dosage in cancer

Nazari

Skandari

2020

IET Systems Biology

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“…For example, some of the newest works on stabilization of fractional-order chaotic systems can bee seen in Balootaki et al (2020), Liu and Ma (2020), Handa and Sharma (2019), and Mobayen et al (2019). A new approach to design asymptotically stabilizing control and adaptive control has been noted in Noori Skandari and Nazemi (2018). The pseudo-state stabilization problem of fractional-order nonlinear systems has attracted the attention of some researchers (see, for example, Ding et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

On asymptotically stabilizing control of nonlinear fractional control systems using an optimization scheme

Yavari

Nazemi

2021

Transactions of the Institute of Measurement and Control

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In this paper, stabilization of the nonlinear fractional order systems with unknown control coefficients is considered where the dynamic control system depends on the Caputo fractional derivative. Related to the nonlinear fractional control (NFC) system, an infinite-horizon optimal control (OC) problem is first proposed. It is shown that the obtained OC problem can be an asymptotically stabilizing control for the NFC system. Using the help of an approximation, the Caputo derivative is replaced with the integer order derivative. The achieved infinite-horizon OC problem is then converted into an equivalent finite-horizon one. According to the Pontryagin minimum principle for OC problems and by constructing an error function, an unconstrained minimization problem is defined. In the optimization problem, trial solutions are used for state, costate and control functions where these trial solutions are constructed by using a two-layered perceptron neural network. A learning algorithm with convergence properties is also provided. Two numerical results are introduced to explain the main results.

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“…Moreover, for such systems, designing a stabilizing control to transfer the state variable of system to an equilibrium point can be formulated as an fractional IHOC problem. In fact, we can generalize the approach 14 to fractional systems, which can be led to a fractional IHOC problem.…”

Section: Introductionmentioning

confidence: 99%

Pseudospectral method for fractional infinite horizon optimal control problems

Yang

Skandari

2020

Optim Control Appl Methods

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Summary Up to now, several numerical methods have been presented to solve finite horizon fractional optimal control problems by researchers, while solving fractional optimal control problems on infinite domain is a challenging work. Hence, in this article, a numerical method is proposed to solve fractional infinite horizon optimal control problems. At the first stage, a domain transformation technique is used to map the infinite domain to a finite horizon. Also, fractional derivative defined on an unbounded domain is converted into an equivalent derivative on a finite domain. Then, a new shifted Legendre pseudospectral method is utilized to solve the obtained finite problem and a nonlinear programming problem is suggested to approximate the optimal solutions. Finally, some numerical examples are given to show the efficiency of the method.

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A new approach to design asymptotically stabilizing control and adaptive control

Cited by 6 publications

References 39 publications

Pseudo‐spectral method for controlling the drug dosage in cancer

Pseudo‐spectral method for controlling the drug dosage in cancer

On asymptotically stabilizing control of nonlinear fractional control systems using an optimization scheme

Pseudospectral method for fractional infinite horizon optimal control problems

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