Sir Alistair MacFarlane was a gifted engineer with a fascination for feedback control systems from his industrial experience on radar systems through to his university research on multivariable control system design. He managed to excel in both practical design and mathematical analysis. He was also exceptionally effective, charismatic and visionary in leadership positions at both Cambridge and Heriot-Watt universities.

We describe an online ‘continuing education’ course on Control Engineering for graduates of any branch of Engineering or other scientific discipline. The course runs mostly asynchronously over 8 weeks, with the expectation that each student will devote 7–9 hours per week to it. Initially, motivational material is presented in the form of examples of control systems and their benefits. The feedback structure is emphasised, but feedforward, cascade and multivariable struc-tures are also discussed. Sensors and actuators are introduced, several examples of each being given. Mathematical analysis is introduced after a qualitative understanding of feedback has been established. Emphasis is given throughout the course to PID controllers, including their implementation and limitations, as well as approaches to tuning them. ‘Classical’ frequency-domain analysis and design methods for SISO systems are presented and emphasised. Later parts of the course cover more advanced material such as state feedback, observers, and LQG controllers. More advanced material, including MPC, adaptive and robust control, is introduced very briefly. The course is assessed by graded assignments based on a nonlinear model of an industrial process. Students develop a working knowledge of Matlab and Simulink software during the course. Keywords: Continuing education, online course, mature stu-dents, control engineering.

This paper uses an SEIR model to study in detail what we have learned, over the first eighteen months of the Covid-19 pandemic, about the optimal duration of lockdown and the optimal severity of subsequent policy. We produce two new sets of results. First, we show that the inevitable trade-off between deaths and economic costs may be non-convex. This means that the optimal policy choice may be discontinuous: a small increase in the value of life can imply that lockdown should last much longer and that subsequent policies should be much more severe. Second, we examine the effectiveness of test-and-trace and vaccination. We show that these are complementary policies: the former exerts its main effect on infections and deaths immediately, whereas the latter acts more gradually but ultimately more effectively. We use data from the UK, beginning at a time when there was a spike in infections. We optimise over a two-year period, and assume that in each ten-day period there is a continuum of possible interventions, ranging from no intervention to full lockdown. The SEIR model is highly non- linear, and the resulting intertemporal optimisation problem is non-convex, meaning that sophisticated control-engineering techniques are needed to find an optimal solution.

In this paper, a recursive t-distribution noise model based maximum likelihood estimation algorithm for discrete-time dynamic state estimation is proposed. The proposed estimator is robust to outliers because the "thick tail" of the t-distribution reduces the effect of large errors in the likelihood function. A computationally efficient recursive algorithm is derived using the influence function. As the t-distribution reduces to the Gaussian distribution when its degree of freedom tends to infinity, the proposed estimator reduces to the Kalman filter. The mean squared error is used to evaluate the performance of the proposed estimator. Compared with the Kalman filter, the proposed estimator is more robust to outliers in the process and measurement noise. Simulations show that for the particle filter to give a better mean squared error, its computational time is two orders of magnitude slower than the proposed estimator.

In the United Kingdom, as elsewhere, there has been a debate on how to escape from lockdown without provoking a resurgence of the Covid-19 disease. This paper presents a simple cost-benefit analysis inspired by optimal control theory, incorporating an SEIR model of disease propagation. Our calibration accords with UK experience and simulations start from the beginning of January 2021. The optimal path for government intervention is computed under different assumptions about the value of life. We examine how the test & trace system and vaccination affect this optimal path and show that these policies are complements. Test & trace has most effect at the beginning when prevalence is high, whereas vaccination only affects infections gradually. Comparing optimal paths, we show that economic cost is much lower under vaccination alone than under test & trace alone. Deaths, in contrast, are somewhat higher under vaccination. In general, the greater is the value of life, the longer is the optimal lockdown. Under certain conditions, this relationship is discontinuous: a small increase in the value of life leads to a jump in the optimal length of lockdown.

This paper investigates an optimal scheduling method for the operation of combined cycle gas turbines (CCGT). The objective is to minimize the CO2 emissions while supplying both electrical and thermal loads. This paper adopts a detailed model of the units in order to relate the heat and power outputs. The grid constraints as well as system losses are considered for both the electrical and thermal systems. Finally, the optimal power dispatch lies on the hybridization of a mixed integer linear programing scheduling with a greedy search method. Different sets of simulations are run for a small 5-bus test case and a larger model of Jurong Island in Singapore. Several load levels are considered for the heat demand, and the impact of the steam pipe capacities is highlighted.

AbstractThe British government has been debating how to escape from the lockdown without provoking a resurgence of the COVID-19 disease. There is a growing recognition of the damage the lockdown has caused to economic and social life. This paper presents a simple cost–benefit analysis inspired by optimal control theory and incorporating the SIR model of disease propagation. It also reports simulations informed by the theoretical discussion. The optimal path for government intervention is computed under a variety of conditions. These include a cap on the permitted level of infection to avoid overload of the health system, and the introduction of a test and trace system. We quantify the benefits of early intervention to control the disease. We also examine how the government’s valuation of life influences the optimal path. A 10-week lockdown is only optimal if the value of life for COVID-19 victims exceeds £10m. The study is based on a standard but simple epidemiological model, and should therefore be regarded as presenting a methodological framework rather than giving policy prescriptions.

Techniques known as Nonlinear Set Membership prediction, Lipschitz Interpolation or Kinky Inference are approaches to machine learning that utilise presupposed Lipschitz properties to compute inferences over unobserved function values. Provided a bound on the true best Lipschitz constant of the target function is known a priori they offer convergence guarantees as well as bounds around the predictions. Considering a more general setting that builds on Hoelder continuity relative to pseudo-metrics, we propose an online method for estimating the Hoelder constant online from function value observations that possibly are corrupted by bounded observational errors. Utilising this to compute adaptive parameters within a kinky inference rule gives rise to a nonparametric machine learning method, for which we establish strong universal approximation guarantees. That is, we show that our prediction rule can learn any continuous function in the limit of increasingly dense data to within a worst-case error bound that depends on the level of observational uncertainty. We apply our method in the context of nonparametric model-reference adaptive control (MRAC). Across a range of simulated aircraft roll-dynamics and performance metrics our approach outperforms recently proposed alternatives that were based on Gaussian processes and RBF-neural networks. For discrete-time systems, we provide guarantees on the tracking success of our learning-based controllers both for the batch and the online learning setting.

This paper presents a self-triggered MPC controller design strategy for linear systems with state and input constraints. Based on the so-called relaxed dynamic programming inequality, the synthesis procedure determines both the updated MPC control action and the next triggering time. The resulting self-triggered MPC control law preserves stability and constraint satisfaction and also satisfies a certain specified performance requirement without requiring stabilizing terminal constraints. A robust self-triggered MPC scheme, based on the tube-MPC idea, is also presented for linear systems with persistent bounded additive disturbances. Simulation examples illustrate the effectiveness of our proposed self-triggered MPC scheme.

This paper presents a robust self-triggered MPC controller design strategy for constrained linear systems with persistent bounded additive disturbance. Based on the so-called relaxed dynamic programming inequality and tube-MPC ideas, at a triggering time, the synthesis procedure allows us to determine both the updated MPC control action and the next triggering time. The resulting robust self-triggered MPC control law preserves stability and constraint satisfaction and also satisfies a certain specified performance requirement without requiring stabilizing terminal constraints. A simulation example illustrates the effectiveness of our proposed robust self-triggered MPC scheme.

SummaryA “general dissipativity constraint” (GDC) is introduced to facilitate the design of stable feedback systems. A primary application is to MPC controllers when it is preferred to avoid the use of “stabilising ingredients” such as terminal constraint sets or long prediction horizons. Some very general convergence results are proved under mild conditions. The use of quadratic functions, replacing GDC by “quadratic dissipativity constraint” (QDC), is introduced to allow implementation using linear matrix inequalities. The use of QDC is illustrated for several scenarios: state feedback for a linear time‐invariant system, MPC of a linear system, MPC of an input‐affine system, and MPC with persistent disturbances. The stability that is guaranteed by GDC is weaker than Lyapunov stability, being “Lagrange stability plus convergence.” Input‐to‐state stability is obtained if the control law is continuous in the state. An example involving an open‐loop unstable helicopter illustrates the efficacy of the approach in practice.

This paper presents an optimal management (OM) strategy for distributed generation (DG) planning studies. The objective is the reduction of the CO2 emissions for the power generation on Jurong Island in Singapore. Different DG resources are investigated with solar panels, energy storage units, small gas turbines as well as controllable loads in addition to the centralized generation already in site. Each of those resources is modeled in an optimal scheduling procedure that furtherly allows to test several DG configurations (i.e. different types/sizes/sites) with regards to the CO2 emissions. The paper mainly focuses on the implementation of the OM and the main challenge is to avoid prohibitive computational times, which is tackled thanks to two approaches. At first, a linearization of the line losses with a modified DC power flow is considered while optimizing the system management over a representative day. A generic clustering method is then developed along with a sequential optimal management (S-OM) lying on both nodal and zonal representations of the electrical network. Different validation tests are performed as well as sets of simulations with several DG configurations. The optimal DG planning procedure itself is not in the scope of that paper and will be part of further developments.

Methods known as Lipschitz Interpolation or Nonlinear Set Membership regression have become established tools for nonparametric system-identification and data-based control. They utilise presupposed Lipschitz properties to compute inferences over unobserved function values. Unfortunately, they rely on the a priori knowledge of a Lipschitz constant of the underlying target function which serves as a hyper-parameter. We propose a closed-form estimator of the Lipschitz constant that is robust to bounded observational noise in the data. The merger of Lipschitz Interpolation with the new hyper-parameter estimator gives a new nonparametric machine learning method for which we derive online learning convergence guarantees. Furthermore, we apply our learning method to model-reference adaptive control and provide a convergence guarantee on the closed-loop dynamics. In a simulated flight manoeuvre control scenario, we compare the performance of our approach to recently proposed alternative learning-based controllers.

This paper presents a benchmark to model power systems market mechanisms from the generation mix to the end-users. The objective is to develop a platform that can help solving long-term planning problems. The operation described here is the joined day-ahead (DA) clearing for the wholesale market and the individual optimal scheduling of end-users equipped with distributed solar generation and storage. The implemented methods lie on linear programming whose fast computation allows to consider the decentralized control of an important number of end-users. Several scenarios are investigated with different retail prices and CO 2 mitigation policies as well as different sizes for the decentralized assets at the end-users' level.

The presence of `inverse response' in the step response of a linear time-invariant system is closely associated with the presence of right-half plane zeros. Various links between the two are known: real positive zeros are sufficient to produce inverse response, and an odd number of positive real zeros is necessary and sufficient to give a particular form of inverse response. On the other hand, the presence of complex right-half plane zeros can result in inverse response, or not. The remaining question is whether the presence of right-half plane zeros is necessary for the presence of inverse response. This paper shows that it is not. This is demonstrated by the generation of a number of counter-examples, using an optimisation algorithm and a particular parametrisation of Hurwitz polynomials. We show that the result holds for a strengthened form of inverse response, which we call `ρ-inverse response', and if the system poles are constrained to be real.

This study proposes a new trust-region based sequential linear programming algorithm to solve the AC optimal power flow (OPF) problem. The OPF problem is solved by linearizing the cost function, power balance and engineering constraints of the system, followed by a trust-region to control the validity of the linear model. To alleviate the problems associated with the infeasibilities of a linear approximation, a feasibility restoration phase is introduced. This phase uses the original nonlinear constraints to quickly locate a feasible point when the linear approximation is infeasible. The algorithm follows convergence criteria to satisfy the first order optimality conditions for the original OPF problem. Studies on standard IEEE systems and large-scale Polish systems show an acceptable quality of convergence to a set of best-known solutions and a substantial improvement in computational time, with linear scaling proportional to the network size.

This paper presents an energy management strategy whose objective is the reduction of CO2 emissions of the power system on Jurong Island in Singapore. Distributed Generation (DG), with solar generation, energy storage, small gas turbine as well as controllable loads, is investigated. Such a procedure aims at being integrated in an optimal planning problem to find the best DG configuration and should then correspond to reasonable computational time. Thus a Mixed integer linear programming (MILP) technique is considered for the system simulated over a representative day. A specific attention is attached to the branch losses estimation with a modified DC power flow (DCPF). At first the method is tested for the base case scenario before investigating different configurations for the DG assets. Results are analyzed in terms of carbon emissions and grid losses.

In this paper, we compare the performance of Bernstein global optimization algorithm based nonlinear model predictive control (NMPC) with a power system stabilizer and linear model predictive control (MPC) for the excitation control of a single machine infinite bus power system. The control simulation studies with Bernstein algorithm based NMPC show improvement in the system damping and settling time when compared with respect to a power system stabilizer and linear MPC scheme. Further, the efficacy of the Bernstein algorithm is also compared with global optimization solver BMIBNB from YALMIP toolbox in terms of NMPC scheme and results are found to be satisfactory.

The battery energy storage systems (BESSs) have been increasingly installed in the power system, especially with the growing penetration rate of the renewable energy sources. However, it is difficult for BESSs to be profitable due to high capital costs. In order to boost the economic value of BESSs, this paper proposes a hierarchical energy management system (HiEMS) to aggregate multiple BESSs, and to achieve multimarket business operations. The proposed HiEMS optimizes the multimarket bids considering a realistic BESS performance model, and coordinates the BESSs and manages their state of charge values, according to their price penalties based on dynamically generated annualized cost. By taking part in the energy market and regulation market at the same time, the cost-performance index (CPI) of the BESS aggregation is greatly improved. The impact of photovoltaic generation on system performance and CPI is also studied.

This paper proposes a generic methodology for combined cycle gas turbines (CCGT) modeling. The main objectives are the estimation of the CO2 emissions for specific units and their integration in an environmental power dispatch that considers several plants. At first a design procedure aims at calibrating the model using the sparse information advised by the manufactures. Off-design points are also investigated in order to estimate the CO2 emissions on the whole operating range of the units. The obtained results show a good consistency with the emission coefficients found in the literature for that type of units. Then those carbon costs are used as input parameters for a unit commitment problem (UC). The Mixed Integer Linear Programming (MILP) formulation minimizes the global emissions for a set of different units on Jurong Island in Singapore. The grid emission factor finally obtained for the simulated network displays values close to the registered field data which validates the developed model.