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Received: date / Accepted: date
Abstract
A novel algorithm **for** the **control** synthesis **for** **nonlinear** switched sys- tems is presented in this paper. Based on an existing procedure of state- space bisection and made available **for** **nonlinear** **systems** with the help of guaranteed integration, the algorithm has been improved to be able to con- sider longer patterns of modes with a better pruning approach. Moreover, the use of guaranteed integration also permits to take bounded perturba- tions and varying parameters into account. It is particularly interesting **for** safety critical applications, such as in aeronautical, military or med- ical fields. The whole approach is entirely guaranteed and the induced controllers are correct-by-design. Some experimentations are performed to show the important gain of the new algorithm.

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2.5 Discussions
This chapter introduced the case study building in the thesis, the CCHT houses. They were three- storey twin houses, selected to represent the typical single-family dwelling in Canada. The detailed whole building **model** was built in TRNSYS and the main TRNSYS modules such as the basement and HVAC system were presented. The **model** calibration was conducted with historic measured data; the calibration method and the analysis of the calibration results were also illustrated. The uncertainty on some key parameters and the lack of detailed (sub-hourly) measurements made this calibration study difficult; the results, however, showed a good agreement with measured values. They were well below the targets suggested by ASHRAE Guideline 14 **for** calibrated simulations **for** monthly values, and fairly close **for** hourly values. Fine-tuning parameters of the **model** to reduce the energy use gap between simulation and measurements was not pursued in this study, because the initial goal was not only calibrating the energy use, but also the space temperatures. The dynamic results showed that the calibrated **model** could capture the temperature variations in the space quite well. This is particularly important **for** the study because the **model** will be used **for** **control** purpose in the **following** chapters.

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Modern power grids contain more and more complex dynamic elements, most of the times based on power electronics. This is the case of the HVDC links. They are also active elements which have an impact on the neighborhood of the AC network in which they are inserted. Particularly, HVDCs controls may affect the transient stability of the near zone (see, e.g., [1]). This impact was optimized in [2] and [3] by using an extended **control** **model**. However, as this **model** captures several grid dynamics in addition to the ones of the HVDC link, its order may be high. This situation is encountered in many other power **systems** applications. **For** example, analysis and damping of inter-area modes of a grid needs a **model** of the whole synchronous zone which results in high-order mathematical objects. Another typical example is the so-called secondary regulations (voltage and frequency) **for** which a global vision of the system is also necessary.

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Keywords-Autonomic Computing, **Model**-Driven Engineer- ing, Software Architecture
I. I NTRODUCTION
The 24/7 deployment of distributed **systems** is dramati- cally increasing the complexity and maintenance costs of software **systems**. The ability to adapt then becomes crucial **for** such **systems**. Autonomic computing is a promising way to organize self-adaptive **systems**. This approach aims at realizing computing applications that can dynamically adjust themselves to accommodate changing environments and user needs with minimal or no human intervention [1]. The engineering of such **systems** in the large is rather a challenging task. It is hard to find an appropriate **model** that controls the adaptation itself [2]. Its implementation being generally integrated in a feedback **control** loop, developing several adaptive behaviors necessitates to reason on them, at least to obtain an appropriate coordination between them. Moreover, engineering in the large obviously needs some reuse capabilities on loops or more likely, on elements composing the loops [3].

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Dual Particle Output Feedback **Control** based on Lyapunov drifts **for** **nonlinear** **systems**
Emilien Flayac, Karim Dahia, Bruno H´eriss´e, and Fr´ed´eric Jean
Abstract— This paper presents a dual receding horizon out- put feedback controller **for** a general non linear stochastic sys- tem with imperfect information. The novelty of this controller is that stabilization is treated, inside the optimization problem, as a negative drift constraint on the **control** that is taken from the theory of stability of Markov chains. The dual effect is then created by maximizing information over the stabilizing controls which makes the global algorithm easier to tune than our previous algorithm. We use a particle filter **for** state estimation to handle nonlinearities and multimodality. The performance of this method is demonstrated on the challenging problem of terrain aided navigation.

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In fact, PBC has a practical limitation **for** continuous-time **systems** if it is applied as proposed **for** discrete-time **systems** [21], the need of future state values in real-time. In [28] we proposed the approxi- mate Prediction-Based **Control** (aPBC) with a methodology based on the implicit Runge-Kutta method and state estimation applied to predict future states **for** the free system in real-time based on system **model**. The authors claim that aPBC is the continuous-time applicable version of PBC because it uses prediction and stabilizes free system UPOs, ideally, vanishing steady state **control** effort. In counter- part, predicting future states has some drawbacks because the proposed future state prediction scheme requires an increase in the closed-loop system order and consequently computational power **for** numerical integration. Moreover, it is also subjected to prediction **model** and real system mismatch and integration method precision **for** application.

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Predictive **Control** Based on **Nonlinear** Observer **for** Muscular Force and Fatigue **Model**
T.Bakir 1 , B. Bonnard 2 and S. Othman 3
Abstract— The Functional Electrical Stimulation (FES) is used in the case of neurological disorders (paralyzed muscles) or the muscle reinforcement (sportsmen). A recent **model** was proposed coupling a force **model** and a fatigue **model**. Based on the specific structure of the **model**, we present a predictive **control** scheme using online estimation of the fatigue variables with a **nonlinear** observer. It is numerically tested in a preliminary study.

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This thesis presented a tube Model Predictive Control framework for nonlinear systems that have uncertain dynamics and are subject to unknown external disturbances. [r]

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First, this class of functions uniformly approximate any continuous **nonlinear** function
deﬁned over a compact domain R n (see [42]). Moreover, the canonical expression in-
troduced in [42] uses the minimum and exact number of parameters, and it is the ﬁrst PWL expression able to represent PWL mappings in arbitrary dimensional domains. As a consequence of this, an eﬃcient characterization is obtained from the viewpoint of memory storage and numerical evaluation [26]. Second, the approximation can be used in real implementations; the points taken from the **nonlinear** **model** may be replaced by points taken from sensors or data directly from the process. Thus, it addresses the problem of ﬁnding a PWL approximation of system where a reasonable number of measure samples of the vector ﬁeld is available (regression set) [98]. Third, this alternative approach deals with an approximation which is easier to handle than the **nonlinear** **model**. In fact, it might use many tools developed **for** hybrid **systems** –e.g., the MLD **model** based approach [16]– since algorithms **for** translating MLD **systems** into PWL **systems** are available [15], [102]. Finally, this CPWL is used in a **model** based **control**, termed probing **control** in [68], being a ﬁrst step development a hybrid probing **control**. The task of the controller is to determine, at every instant, the best **control** action (the best feed substrate) based on the compilation of the sensor’s on-line information (or **for** the **nonlinear** **model**). The fact that the probing strategy **for** feedback **control** requires a minimum of process knowledge is exploited in [7]. This work refers to a probing **control** as it is presented in [7] **for** E. coli. Short pulses to the feed rate are added, and taking into account the system response, the pulse is increased or decreased according with the tuning rule. The probing **control** strategy avoids acetate accumulation while maintaining a high growth rate [7], [101]. The main contribution of Chapter 4 is a hybrid dynamical **model** using orthonor-

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Near-Optimal Strategies **for** **Nonlinear** and Uncertain Networked **Control** **Systems**
Lucian Bus¸oniu Romain Postoyan Jamal Daafouz
Abstract—We consider problems where a controller commu- nicates with a general **nonlinear** plant via a network, and must optimize a performance index. The system is modeled in discrete time and may be affected by a class of stochastic uncertainties that can take finitely many values. Admissible inputs are constrained to belong to a finite set. Exploiting some optimistic planning algorithms from the artificial intelligence field, we propose two **control** strategies that take into account the communication constraints induced by the use of the network. Both strategies send in a single packet long-horizon solutions, such as sequences of inputs. Our analysis characterizes the relationship between computation, near-optimality, and trans- mission intervals. In particular, the first strategy imposes at each transmission a desired near-optimality, which we show is related to an imposed transmission period; **for** this setting, we analyze the required computation. The second strategy has a fixed computation budget, and within this constraint it adapts the next transmission instant to the last state measurement, leading to a self-triggered policy. **For** this case, we guarantee long transmission intervals. Examples and simulation experiments are provided throughout the paper.

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Despite the large progress in practical applications (see, among them, [11–14]), when considering the problem of a RC-design in the continuous-time domain, many questions are still open. In particular, it is not clear whether an exact (i.e., infinite-dimensional) RC-scheme can be used (from a theoretical point of view) to achieve asymptotic convergence of the desired regulated output. In fact, one of the main limitations of existing continuous-time schemes is that only “boundary information” (namely, the values of the delayed signal at instants t and t + T ) is used **for** **control** purposes. Such a constraint, however, strongly re- stricts the class of **systems** to which a RC-scheme can be applied, that is **nonlinear** **systems** which are strictly input passive (in other words, with a direct feedthrough term). We refer to [1] **for** a proof **for** linear **systems** where it is shown that exponential stability of a (continuous-time) lin- ear system incorporating a pure delay in the RC-scheme can be achieved only **for** **systems** having zero-relative de- gree between the input and the regulated output; alterna- tively, see [15, 16] **for** a proof in the context of **nonlinear** **systems** based on dissipativity operators.

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Anti-windup Compensation **for** **Nonlinear** **Systems** via Gradient Projection: Application to Adaptive **Control**
Justin Teo and Jonathan P. How
Abstract— **Control** saturation is an important limitation in practical **control** **systems** and it is well known that performance degradation or instability may result if this limitation is not effectively addressed. Using ideas from the gradient projection method in **nonlinear** programming, we propose a new anti- windup scheme **for** multi-input, multi-output **nonlinear** dy- namic controllers. The key idea is to project the controller state update law onto the tangent plane of the active saturation constraints. To do this, we first extend the gradient projection method to the continuous-time case that can accommodate multiple **nonlinear** constraints. This is then used **for** anti-windup compensation, resulting in a hybrid controller that switches its state update law over arbitrary combinations of saturating controls. Simulations on a **nonlinear** two-link robot driven by an adaptive sliding mode controller illustrates its effectiveness and limitations.

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ABSTRACT
Gas turbines are now extensively used in aviation, oil and gas applications and power gen- eration. With this increasing use in a diverse range of applications, gas turbine engines are designed to operate in a wide operating envelope. Typically, the ambient temperature can vary substantially from a hot summer day to a cold winter night. In addition, different fuel types may be used. Furthermore, the performance of a turbine engine deteriorates with use because of component degradation caused by erosion and corrosion. These requirements **for** guaran- teed high performance levels while maintaining stability and safe operation with minimum overall cost impose severe challenges on **control** system design. In this dissertation, new ap- proaches **for** gas turbine engine modelling and multivariable advanced controller design are investigated. A **nonlinear** **model** predictive **control** (NMPC) approach based on an ensemble of recurrent neural networks (NN) is utilized to achieve the **control** objectives **for** a Siemens SGT-A65 three spool aeroderivative gas turbine engine used **for** power generation. A novel ensemble method is proposed, which results in an adaptive NN **model**. The simulation results show improvement in accuracy and robustness by using the proposed modelling approach. Also, another important gain is the very rapid execution time (40,5 μs), which can support many real time applications that require **model**-based **control** design.

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Received: 12 May 2016; Accepted: 22 August 2016; Published: 29 August 2016
Abstract: Optimization techniques are typically used to improve economic performance of
batch processes, while meeting product and environmental speciﬁcations and safety constraints. Ofﬂine methods suffer from the parameters of the **model** being inaccurate, while re-identiﬁcation of the parameters may not be possible due to the absence of persistency of excitation. Thus, a practical solution is the **Nonlinear** **Model** Predictive **Control** (NMPC) without parameter adaptation, where the measured states serve as new initial conditions **for** the re-optimization problem with a diminishing horizon. In such schemes, it is clear that the optimum cannot be reached due to plant-**model** mismatch. However, this paper goes one step further in showing that such re-optimization could in certain cases, especially with an economic cost, lead to results worse than the ofﬂine optimal input. On the other hand, in absence of process noise, **for** small parametric variations, if the cost function corresponds to tracking a feasible trajectory, re-optimization always improves performance. This shows inherent robustness associated with the tracking cost. A batch reactor example presents and analyzes the different cases. Re-optimizing led to worse results in some cases with an economical cost function, while no such problem occurred while working with a tracking cost.

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Periodic event-triggered **control** **for** **nonlinear** networked **control** **systems**
W. Wang, R. Postoyan, D. Neˇsi´c and W.P.M.H. Heemels
Abstract—Periodic event-triggered **control** (PETC) is an ap- pealing paradigm **for** the implementation of controllers on plat- forms with limited communication resources, a typical example being networked **control** **systems**. In PETC, transmissions over the communication channel are triggered by an event generator, which depends solely on the available plant and controller data, and is only evaluated at given sampling instants to enable its digital implementation. In this paper, we consider the general scenario where the controller communicates with the plant via multiple decoupled networks. Each network may contain multiple nodes, in which case a dedicated protocol is used to schedule transmissions among these nodes. The transmission instants over the networks are asynchronous and generated by local event generators. At given sampling instants, the local event generator evaluates a rule, which only involves the measurements and the **control** inputs available locally, to decide whether a transmission is needed over the considered network. **Following** the emulation approach, we show how to design the local triggering generators to ensure input-to-state stability and L p -stability **for** the overall

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ples of feedback-**control** **for** the analysis of cyber-physical **systems** (CPS). FC-SSC uses stochastic system identification to learn a CPS **model**, im- portance sampling to estimate the CPS state, and importance splitting to **control** the CPS so that the probability that the CPS satisfies a given property can be efficiently inferred. We illustrate the utility of FC-SSC on two example applications, each of which is simple enough to be easily understood, yet complex enough to exhibit all of FC-SCC’s features. To the best of our knowledge, FC-SSC is the first statistical system checker to efficiently estimate the probability of rare events in realistic CPS ap- plications or in any complex probabilistic program whose **model** is either not available, or is infeasible to derive through static-analysis techniques.

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The adaptive controller has the capability to quickly learn and adapt to parameter uncertainties. Like the sliding control, the explicit model of the nonlinear structure i[r]

The SISO designs for the MACE test article in Chapter 3 imply that the MM technique effectively enhances robust stability and performance of compensators for two [r]

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