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Questions tagged [adaptive-control]

This tag is for questions relating to Adaptive control. The adaptive controller is to be designed so that the plant output follows the model output as closely as possible. It is the capability of the system to modify its own operation to achieve the best possible mode of operation. The area of adaptive systems has been one of the most active in identification and control theory of the past decade.

A general definition of adaptive control implies that an adaptive system must be capable of performing the following functions: providing continuous information about the present state of the system or identifying the process; comparing present system performance to the desired or optimum performance and making a decision to change the system to achieve the defined optimum performance; and initiating a proper modification to drive the control system to the optimum. These three principles—identification, decision, and modification—are inherent in any adaptive system.

Applications : Adaptive control is the identification and control of the system. In some applications we have to identify the system and to adjust the control in accordance with the model which is supposed to be approaching the true system during the process of identification. This is why there has been tremendous interest in identification and adaptive control for stochastic systems from both theorists and practitioners, in particular, mathematicians, engineers, economists, biologists, environmental scientists and others.

References:

" Mineral Processing Design and Operations" by A. Gupta and D.S. Yan https://www.britannica.com/technology/control-system#ref199542 https://en.wikipedia.org/wiki/Adaptive_control

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What adaptive controller can be used in embedded system with low RAM?

This is not a question for data science, hardware or programming languages. This is a more practical question about adaptive control for embedded systems, but still a math question. I have tried to apply matrix algebra for subspace identification…
euraad
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MIT rule VS Lyapunov design - Adaptive Control

I wonder what's the difference between MIT rule and Lyapunov design when it comes to adaptive control law? As I get it, MIT rule is more like "transfer function"-based control system and Lyapunov design is more like "state space model"-based control…
euraad
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Control a non-affine system

I have a question about the control of a non-affine system. Here is my system $\dot{x} = a(u) + b(u) . u$ \begin{equation}\label{a_beta} a(u) = 0.22 \left( \frac{116(u^3 + 1)-4.06 \lambda }{(\lambda + 0.08u)(u^3 + 1)} -5 \right) \exp \left(…
Ehsan Aslmostafa
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Finite-time criterion for ODE

In article Finite-Time Stability of Continuous Autonomous Systems i found this [page 4]. That's what I don't understand: Can (2.7) $\dot{y}(t)=-k \cdot {\rm sign}(y(t)) \cdot \lvert y(t) \rvert^{\alpha}$ be reformulated as a condition for…
ayr
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How to design/add a new controller to a system without breaking the existing controller in the system?

Please help me to find related topics/books for this problem: For example, assume we have a water heater, and a tank of water. We can design a controller to heat the water in the tank and keep it in a certain temperature. This can be achieved by a…
Alex
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Control that stabilizes an uknown unstable equilibrium point?

Give a non-linear ( if it helps, multi-linear ) system for the variable with $\mathbf{Z} = [\mathbf X_1, \ldots, \mathbf{X_n} ]^T$: $$ \dot{\mathbf{Z}} = F ( \mathbf{Z}, \mathbf{u} ) $$ and an unknown equilibrium point $\mathbf{Z^*}$ (i.e. 0 = F…
shnnnms
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In-depth example or implementation of adaptive control (direct/indirect MRAC)?

I have seen some examples where adaptive control is used to counter sudden changes in a system with great success. Since I find the subject quite interesting, I would like to learn how to actually implement an adaptive control loop, with the end…
Leo
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Nonlinear geometric control for beginners

Please advise literature or articles on nonlinear geometric control (for beginners). Preferably with computational examples. I want to study this topic, but I do not know where to start. Remark: Thanks to everyone who advised the book. I have not…
ayr
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What's the difference between Generalized Predictive Control and Model Predictive Control?

As I know, the Generalized Predictive Control(GPC) is older than Model Predictive Control(MPC). But what is the real difference between them? I know that GPC contains some kind of system identification, which make GPC as an adaptive controller. But…
euraad
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How do I place the poles and zeros form a disired system? Adaptive control

If I have a transfer function of a system $G(s)$ $$G(s) = \frac{4 - 2s}{4 + 0.8s + s^2}$$ $G(s)$ has the poles and zeros and is a stable system. And the step answer look like. It has a delay as you can see, a.k.a non-minimum phase system. I want…
euraad
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What is the exact connection between PID and state feedback controllers?

Suppose we are dealing with a control problem where the reference trajectory is $0$, then the PID controller is a function, $$u = K_1 x + K_2 \dot x + K_3 \int_0^t x dt$$ where $x$ is your state. But this looks almost exactly like state feedback…
Your neighbor Todorovich
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Model Reference Adaptive Control for Linear Algebraic Plants

This is a homework problem from my adaptive control course: Given the plant $y_p = a_pu(t)$ ($a_p\neq 0$) and the reference model $y_m = a_mr(t)$, where $r(t)$ is bounded and continuous. Design a differentiator free control $u(t)$ such that all…
ArGenya
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Issue with definition of adaptive control and its classification

I have a question about the definition of adaptive control, since I´m researching about making a model-free adaptive control system. I will appreciate your help. The definition I found says that an adaptive control modifies its parameters or…
Pablo Andres Martin Gonzalez
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Adaptive step size for nonlinear static problem

Let's assume $F$ is an external load for a nonlinear static finite element problem. Normally, the problem will not converge if you apply $F$ fully. Instead, we multiply the load $F$ with a scaling factor $\lambda$, solve the problem with a small…
Di Miao
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Nonlinear system with time-optimal control

Given nonlinear system: \begin{cases} \dot{x_1}=x_3+u \\ \dot{x_2}=-x_2+\dot{f} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) \\ \dot{x_4}=-x_4+x_2 \cdot (\frac{16}{\alpha^2}(\sin(\omega t)-\frac{1}{2})) \end{cases} where, $x_1...x_4$ -…
ayr
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