This work develops a tube-based model predictive control (MPC) scheme for quasi-linear parameter-varying (quasi-LPV) systems affected by bounded disturbances and time-varying but measurable scheduling parameters. The controller uses a polytopic model together with a gain-scheduled feedback law to maintain robustness against parameter variations and external disturbances. To describe the terminal region more flexibly, a parameter-dependent terminal cost is introduced. In addition, an auxiliary cost function, evaluated only at the vertices of the polytope, removes the need to update parameters at every prediction step. Although the proposed formulation increases the computational load slightly, it provides stronger disturbance rejection and improved constraint handling. Experiments on a coupled-tank setup demonstrate that the method is both effective and practical for real-time implementation.

In this paper, we address the problem of computing passivity indices-quantitative measures of a system's passivity-due to their significance in controller design. In practical scenarios, the explicit input-output relationship of a system is often unavailable, and only input-output data from simulations or experiments can be accessed. We focus on determining the passivity indices of a discrete linear time-invariant system using optimal input-output samples tailored to the specific property being assessed. Here, passivity indices are formulated as an objective function of an optimization problem. To compute these indices, we introduce prescribed-time gradient flows, which has the property of guaranteed convergence, within a prior chosen time. Notably, the proposed method is data-driven and does not require knowledge of the system's mathematical model, as it relies solely on gradients computed from data. Furthermore, we leverage the feedback interconnection properties of passive systems to ensure both asymptotic and finite-time stability of the discrete-time system, using only the computed passivity indices. Specifically, stabilization is achieved by employing input feedforward passive and output feedback passive systems as controllers, again without requiring the explicit model of the system. Simulation results for the coupled tank system shows the effectiveness of the proposed approach.

In model predictive control (MPC), the control input is determined at each instance by formulating and solving an optimisation problem that incorporates real-time measurement updates. Applications characterised by rapid process dynamics often necessitate shorter sampling intervals, which impose stringent requirements on computational consistency. Also, implementing MPC on hardware with constrained computational resources remains a significant challenge. Consequently, the realisation of MPC for such scenarios mandates an appropriate choice of an optimisation algorithm that exhibits consistency in terms of iteration numbers, ensuring optimised solutions within a sampling period in real-time environments. This study introduces the application of an infeasible interior-point barrier algorithm tailored for MPC. The MPC is formulated for linear systems in the condensed framework so that the number of decision variables in the optimisation problem is reduced. The solution algorithm of the optimisation problem is formulated on primal-dual conditions. The proposed algorithm is evaluated in real-time on a coupled tank system. Both the state and output feedback MPC are implemented that demonstrate consistent iteration count throughout its runtime. Comparative performance analyses with other methodologies are conducted elucidating the trade-offs inherent in different approaches.

This paper proposes a Model Predictive Control (MPC) strategy for a class of Quasi-Linear Parameter-Varying (quasi-LPV) systems characterized by a measurable time-varying parameter. The core of the proposed quasi-LPV-MPC controller lies in the utilization of a polytopic representation along with a gain-scheduled controller. A terminal cost that depends explicitly on the scheduling parameter is used. However, for the implementation, a complementary cost function is used to frame the optimization problem at each vertex level so that the requirement of updating the varying parameters over the prediction horizon is relaxed. Though the resulting suboptimal controller involves more computational burden, the proposed method demonstrates improvement in control performance over traditional MPC schemes. Experimental validation on a cascaded coupled tank system underscores the practical efficacy of the proposed quasi-LPV-MPC controller, while simulation studies on a twin rotor multi-input multi-output system serve as an additional demonstration example case. Comparative performance evaluations against both linear and nonlinear MPCs clearly illustrate that the quasi-LPV-MPC offers better control precision, adaptability, and the overall system responsiveness, thus positioning it as an effective solution for quasi-LPV systems.

In this paper, we utilise the prospect of integrating the idea of predefined upper bound of settling time-based stable gradient flow dynamics and projected gradient techniques to solve convex optimisation problems with linear equality constraints. We propose a projected gradient flow algorithm with a predefined-time convergence property, where the upper bound of settling time can be selected a priori. A perturbed projected gradient flow is also studied within the framework of input-to-state stability. Examples based on linear least squares and resource allocation problems (RAP) are solved using the proposed algorithm and simulation results are also compared with finite/fixed-time stable projected gradient flows.

As technology advances and the utilization of renewable energy sources (RESs) increases, peer-to-peer (P2P) energy trading has become a noteworthy strategy in the local energy market. This work introduces an integrated transactive energy market with the active participation of distributed generations (DGs) and distribution system operator (DSO) and facilitates P2P energy trading models for flexible loads and RES equipped buildings. A distribution locational marginal price (DLMP) and modified Nash bargaining solution strategy are employed to ensure fair distribution of economic benefits. Equilibrium strategies for all participants are achieved through a decentralized approach that preserves their privacy. For each group of buildings, a virtual community (VC), a shareable battery energy storage is integrated, and uncertainties concerning RESs are addressed using Hong's 2m point estimation method. This paper also proposes an algorithm for real-time execution to ensure the maintenance of network constraints and energy balance based on day-ahead market commitments and RES deviations. A real-time digital simulator (RTDS) is used to validate the energy sharing.

In this paper, we propose continuous-time algorithms for tracking the optimal trajectory of time-varying optimization problems with time-varying constraints in a predefined time, where the time of convergence is selected a priori. A robust Newton-like approach is developed for the cases, where the exact knowledge of the rate of change of the gradient of objective function is unknown. Levenberg-Marquardt-like algorithm is proposed for the cases when the Hessian of the objective function is singular or near singular. Lyapunov-based convergence analysis is discussed for the proposed algorithms. Simulation results for time-varying optimization problems show the efficacy of the proposed approach. We demonstrate the applicability of the proposed method through its use in a collision-free robot navigation problem.

Peer-to-peer (P2P) exchanges provide opportunities for prosumers to meet their energy needs cost-effectively with the effective utilization of renewable energy sources (RES). Along with the benefits, P2P energy trading also raises issues in distribution network operations. The proposed framework has the potential to handle transactions in regard to network constraints by leveraging the benefits of dynamic utilization-based charges for network usages and power pricing structures. This work proposes a novel P2P energy trading framework comprising virtual communities (VCs) made by grouping buildings located on a particular bus. A cooperative game is formulated for inter- and intra- bus energy trading. A battery energy storage system (BESS) is present in each VC, and a stochastic model is used for coping with the uncertainties related to RESs. In this work, each player’s individual problem is decoupled to achieve equilibrium in a decentralized manner to avoid security and privacy issues. This research focuses on the significant reduction in the net energy cost of the buildings in the presence of uncertain renewable energy generations by taking advantage of the load variability of buildings present on the same and different buses without violating any network constraints and raising any privacy concerns. The proposed framework reduces the building cost by 21.87%.

In this paper, we propose a new passivity-based controller design technique for discrete-time fully actuated systems. The controller establishes finite-time and fixed-time convergence of dynamical system trajectories to an equilibrium state. A new form of a dissipation function, selected a priori, is introduced to design a feedback control rule to achieve such convergence properties. An energy shaping and damping injection methodology is extended to achieve non-asymptotic stabilization. A numerical example to validate the proposed methods is provided.

With the increase in the use of renewable energy sources (RESs) and advances in technologies, peer-to-peer (P2P) energy trading is emerging as a promising approach to the local energy market. This work proposes a virtual community (VC) based P2P energy trading for buildings equipped with RES and flexible loads. A modified Nash bargaining solution is used for fair incentive distribution in the cooperative game. In this work, the equilibrium strategies of all players are obtained using a privacy-preserving decentralised approach. Shareable battery energy storage is considered in each VC, and Hong's 2m point estimation method is used to cope with the uncertainties associated with RESs.

The power trading model considering operating agents at different levels, such as distribution utility, microgrid operators, and end-users allows for efficient energy resource coordination and effective utilization. The simultaneous and hierarchical optimization of multiple agents has not yet been attempted. The techno-economic aspects can be accomplished more effectively if the energy management framework considers hierarchically coordinated decision-making of all agents. The decisions of all agents are interlinked and can be realized with a hierarchical Stackelberg game model. This article proposes an energy management framework incorporating a three-level hierarchical decision approach, through which multiple operating agents can actively participate in energy management to achieve their respective goals. In this framework, a game-theoretic dynamic pricing scheme is used to enable the interaction of distribution utility and microgrid operators as well as the microgrid operators and end-user aggregators. This arrangement enables end-user aggregators to negotiate adequately with microgrid operators. This article also investigates the impact of risk-averse and risk-seeker decisions of microgrid operators on the operating cost of distribution utility. The numerical results establish the effectiveness of the proposed framework and demonstrate that the proposed participatory strategy can improve economic benefits with technical aspects, such as lower peak demand and improved voltage profiles.

Peer-to-peer (P2P) trading is essential in maximising the benefits of renewable integration. The paper proposes a novel framework for economic benefit through P2P trading among buildings at different geographical locations. The number of transactions is reduced by grouping the buildings into virtual communities (VCs) based on their geographical locations. A non-cooperative game is formulated and solved in a decentralised manner for the energy management of individual buildings, building-to-building (B2B) energy exchange, building-to-community (B2C) energy exchange, energy management of the respective VC, and community-to-community (C2C) energy exchange. Load shifting is used to incorporate demand-side management. Cloud computing-based proposed algorithm is used for determining the energy profile and prices for each internal transaction (B2B, B2C, and C2C) separately to encourage the participation of each building by benefiting them appropriately and avoiding privacy/security issues normally arising in any data-centric framework. A shareable battery energy storage system (BESS) is also assumed to be present in each VC. Load shifting is used in the modelling of buildings to incorporate demand-side management.

A game-theory-based optimal and cyber-attack resilient energy scheduling in multiple smart buildings (SBs) framework considering false data injection (FDI) attack has been proposed in this work. The proposed resilient scheduling is based on the consumers’ past behavior, and import and export power between the SBs and grids. An optimal resilient energy scheduling framework is designed considering renewable energy sources (RESs), combined heat and power (CHP) generators, battery storage systems (BSSs), various smart home (SH) appliances, and FDI attack. An iterative algorithm is used to solve a game-theory-based mixed integer quadratic constrained program (MIQCP) problem in the general algebraic model system (GAMS) environment with a CPLEX solver. For identifying the FDI attack and making a resilient scheduling against possible attacks, the proposed technique uses the difference between the actual and forecasted bills as well as maximum change in demand. The impacts of FDI attack which can be detrimental can be avoided, however, there may be a small difference between energy cost without considering FDI attack and energy cost with resilient scheduling.

Peer-to-peer (P2P) energy trading fosters direct energy exchange between prosumers in a cost-effective manner. However, there are many challenges in implementing the P2P framework on a large scale. The prominent one is maintaining the distribution network operation under prescribed limits. This work proposes a novel P2P energy-sharing framework using a modified Nash bargaining-based cooperative game for all buildings hypothetically aggregated as virtual communities (VCs) based on their location in the distribution network. This framework incorporates the active participation of DGs as well as DSO in the local energy market and has the ability to settle transactions with respect to network constraints using dynamic network usage charges and electricity prices. The hypothetical aggregation or grouping reduces the number of transactions resulting in improved computational efficacy. A shareable battery energy storage system (BESS) is also assumed to be present in each VC. The proposed algorithm is based on cloud computing which is able to derive the equilibrium strategies of all players using a privacy-preserving decentralized approach.

This article explores the theory of discrete-time gradient systems that converge in a finite amount of time and are governed by a difference equation with minima. Two algorithms with distinct structures are discussed, both aimed at achieving finite-time stabilization of these systems. These gradient-based algorithms have significant applications in solving optimization problems. Using the finite-time convergent techniques discussed in the article, a quadratic programming problem is solved, and an optimal solution is obtained within a finite time frame. The effectiveness of these proposed methods is demonstrated through simulation results.

Gradient flow systems provide effortless continuous time optimization. Such systems have inherent property that their solutions move in the direction of descent. This paper proposes a modified gradient flow technique to reach optimal point of an objective function within a priori chosen predefined time. A least square estimation problem and a quadratic programming problem are solved using the proposed continuous-time optimization approach. Simulation results of the aforementioned problems show the efficacy of the proposed method. Further, results obtained with predefined upper bound of settling time based approach are compared with the results using fixed-time stable gradient flow scheme.

The decentralized economic scheduling of multimicrogrid is an important aspect in the operational planning of microgrids (MGs). This article proposes an approach to maximize economic benefit among MGs through cooperative scheduling. The cooperative scheduling is achieved via price signals so that MGs are encouraged to share power among themselves for economic benefit. An MG operator generates a time-variable tariff based on energy trading status so that the parking lot operator and distributed battery energy storage system aggregator participate with flexibility in the MG’s energy management. The Shapley value method is used for generating fair price signals. The stochastic Dantzig–Wolfe decomposition is used to solve the resulting optimization problem in a decentralized manner. The uncertainties related to load demand and renewable energy sources are captured using scenario-based methods, whereas the uncertainty associated with plug-in hybrid electric vehicles is modeled using copula theory based estimation. The simulation studies and comparison with the existing methods establish that the proposed approach effectively reduces the total energy cost in a decentralized manner with the minimum amount of information exchange.

To solve the nonconvex constrained optimization problems (COPs) over continuous search spaces by using a population-based optimization algorithm, balancing between the feasible and infeasible solutions in the population plays an important role over different stages of the optimization process. To keep this balance, we propose a constraint handling technique, called the $\upsilon $ -level penalty function, which works by transforming a COP into an unconstrained one. Also, to improve the ability of the algorithm in handling several complex constraints, especially nonlinear inequality and equality constraints, we suggest a Broyden-based mutation that finds a feasible solution to replace an infeasible solution. By incorporating these techniques with the matrix adaptation evolution strategy (MA-ES), we develop a new constrained optimization algorithm. An extensive comparative analysis undertaken using a broad range of benchmark problems indicates that the proposed algorithm can outperform several state-of-the-art constrained evolutionary optimizers.

With the emerging role of the Peer-to-peer (P2P) energy sharing concept in effectively utilising renewable energy resources, the need for a suitable incentivising/pricing method is also increasing. In this work, a cooperative game is formulated in a community of buildings where a community battery energy storage system (CBESS) acts as a player along with other buildings. With the help of generalised Nash bargaining, the problem is formulated and minimised in a decentralised way using ADMM. "Hong's 2m point estimate method" is used for stochastic modelling renewable generation uncertainties. Suitable incentives are decided to motivate the players to engage in this game of P2P energy sharing. Along with the incentives, prices per unit of energy shared are also calculated. When compared, both methods give almost the same results.

This chapter is based on a recently published paper [9] of authors of this chapter in which a method for solving bound-constrained non-linear global optimization problems has been proposed. The algorithm obtains a sphere and then generates new trial solutions on its surface. Hence, this algorithm has been named as Spherical Search (SS) algorithm. This chapter starts with an introduction to the SS algorithm and then discusses different components and steps of the algorithm, viz., initialization of population, the concept of a spherical surface, the procedure of generation of trial solutions, selection of new population using greedy selection, stopping criteria, steps of the algorithm, and space and time complexity of the algorithm. Then, the algorithm has been applied to solve 30 bound-constrained global optimization benchmark problems of IEEE CEC 2014 suite and the results of the spherical search algorithm on these benchmark problems have been compared with the results of variants of well-known algorithms such as particle swarm optimization, genetic algorithm, covariance matrix adapted evolution strategy, and Differential Evolution on these problems to demonstrate its performance. Further, the SS algorithm has been applied to solve a model order reduction problem, an example of a real-life complex optimization problem.